Life Mathematics Class 8th Mathematics Term 3 Tamilnadu Board Solution

Class 8^th Mathematics Term 3 Tamilnadu Board Solution

Exercise 1.1

1. There are 5 oranges in a basket of 25 fruits. The percentage of oranges is…
2. 2/25 = _______ %.A. 25 B. 4 C. 8 D. 15
3. 15% of the total number of biscuits in a bottle is 30. The total number of…
4. The price of a scooter was Rs. 34,000 last year. It has increased by 25% this…
5. A man saves Rs. 3,000 per month from his total salary of Rs. 20,000. The…
6. 20% of the total quantity of oil is 40 liters. Find the total quantity of oil…
7. 25% of a journey covers 5,000 km. How long is the whole journey?
8. 3.5% of an amount is Rs. 54.25. Find the amount.
9. 60% of the total time is 30 minutes. Find the total time.
10. 4% sales tax on the sale of an article is Rs. 2. What is the amount of sale?…
11. Meenu spends Rs. 2000 from her salary for recreation which is 5% of her salary.…
12. 25% of the total mangoes which are rotten is 1,250. Find the total number of…
13. The marks obtained by Rani in her twelfth standard exams are tabulated below.…
14. A school cricket team played 20 matches against another school. The first school…
15. Rahim deposited Rs. 10,000 in a company which pays 18% simple interest p.a. Find…
16. The marked price of a toy is Rs. 1,200. The shop keeper gave a discount of 15%.…
17. In an interview for computer firm 1,500 applicants were interviewed. If 12% of…
18. An alloy consists of 30% copper and 40% zinc and the remaining is nickel. Find…
19. Pandian and Thamarai contested for the election to the Panchayat committee from…
20. A man spends 40% of his income for food, 15% for clothes and 20% for house rent…
21. Jyothika secured 35 marks out of 50 in English and 27 marks out of 30 in…
22. A worker receives Rs. 11,250 as bonus, which is 15% of his annual salary. What…
23. The price of a suit is increased from Rs. 2,100 to Rs. 2,520. Find the…

Exercise 1.2

1. Find the Cost price / Selling price.
2. Fill up the appropriate boxes and leave the rest.
3. a bicycle of Rs. 700 with Rs. 50 as overhead charges. Find the S.P. if a profit…
4. a computer table bought at Rs. 1,150 with Rs. 50 as transportation charges.…
5. a table-top wet grinder bought for Rs. 2,560 and an expense of Rs. 140 on…
6. By selling a table for Rs. 1,320, a trader gains 10%. Find the C.P. of the…
7. The cost price of 16 note books is equal to the selling price of 12 note books.…
8. A man sold two articles at Rs. 375 each. On the first article, he gains 25% and…
9. Anbarasan purchased a house for Rs. 17,75,000 and spent Rs. 1,25,000 on its…
10. After spending Rupees sixty thousand for remodeling a house, Amla sold a house…
11. Jai kumar bought a plot of land in the outskirts of the city for Rs. 21,00,000.…
12. A man sold two varieties of his dog for Rs. 3,605 each. On one he made a gain…

Exercise 1.3

1. The discount is always on the _______.A. Marked Price B. Cost Price C. Selling…
2. If M.P. = Rs. 140, S.P. = Rs. 105, then Discount = _______.A.Rs. 245 B.Rs. 25…
3. ______ = Marked Price - Discount.A. Cost Price B. Selling Price C. List Price…
4. The tax added to the value of the product is called ______ Tax.A. Sales Tax B.…
5. If the S.P. of an article is Rs. 240 and the discount given on it is Rs. 28,…
6. The price marked on a book is Rs. 450. The shopkeeper gives 20% discount on it a…
7. A television set was sold for Rs. 5,760 after giving successive discounts of 10%…
8. Sekar bought a computer for Rs. 38,000 and a printer for Rs. 8,000. If the rate…
9. The selling price with VAT, on a cooking range is Rs. 19,610. If the VAT is 6%,…
10. Richard got a discount of 10% on the suit he bought. The marked price was Rs.…
11. The sales tax on a refrigerator at the rate of 9% is Rs. 1,170. Find the actual…
12. A trader marks his goods 40% above the cost price. He sells them at a discount…
13. A T.V. with marked price Rs. 11,500 is sold at 10% discount. Due to festival…
14. A person pays Rs. 2,800 for a cooler listed at Rs. 3,500. Find the discount…
15. Deepa purchased 15 shirts at the rate of Rs. 1,200 each and sold them at a…
16. Find the discount, discount percent, selling price and the marked price.…

Exercise 1.4

1. Find the Amount and Compound Interest in the following cases:
2. Sangeetha borrowed Rs. 8,000 from Alex for 2 years at 121/2% per annum. What…
3. Maria invested Rs. 80,000 in a business. She would be paid interest at 5% per…
4. Find the compound interest on Rs. 24,000 compounded half - yearly for 11/2 years…
5. Find the amount that Dravid would receive if he invests Rs. 8,192 for 18 months…
6. Find the compound interest on Rs. 15,625 for 9 months, at 16% per annum…
7. Find the Principle that will yield a compound interest of Rs. 1,632 in 2 years…
8. Vicky borrowed Rs. 26,400 from a bank to buy a scooter at the rate of 15% p.a.…
9. Arif took a loan of Rs. 80,000 from a bank. If the rate of interest is 10% p.…
10. Find the difference between simple interest and compound interest on Rs. 2,400…
11. Find the difference between simple interest and compound interest on Rs. 6,400…
12. The difference between C. I. and S. I. for 2 years on a sum of money lent at 5%…
13. Sujatha borrows Rs. 12,500 at 12% per annum for 3 years at simple interest and…
14. What sum is invested for 11/2 years at the rate of 4% p.a. compounded half…
15. Gayathri invested a sum of Rs. 12,000 at 5% p.a. at compound interest. She…
16. At what rate percent compound interest per annum will Rs. 640 amounts to Rs.…
17. Find the rate percent per annum, if Rs. 2,000 amounts to Rs. 2,315.25 in an…

Exercise 1.5

1. The number of students enrolled in a school is 2000. If the enrolment increases…
2. A car which costs Rs. 3,50,000 depreciates by 10% every year. What will be the…
3. A motorcycle was bought at Rs. 50,000. The value depreciated at the rate of 8%…
4. In a Laboratory, the count of bacteria in a certain experiment was increasing at…
5. From a village people started migrating to nearby cities due to unemployment…
6. The present value of an oil engine is Rs. 14,580. What was the worth of the…
7. The population of a village increases by 9% every year which is due to the job…

Exercise 1.6

1. Ponmani makes a fixed deposit of Rs. 25,000 in a bank for 2 years. If the rate…
2. Deva makes a fixed deposit of Rs. 75,000 in a bank for 3 years. If the rate of…
3. Imran deposits Rs. 400 per month in a post office as R.D. for 2 years. If the…
4. The cost of a microwave oven is Rs. 6,000. Poorani wants to buy it in 5…
5. The cost price of a refrigerator is Rs. 16,800. Ranjith wants to buy the…
6. The cost of a dining table is Rs. 8,400. Venkat wants to buy it in 10…

Exercise 1.7

1. Twelve carpenters working 10 hours a day complete a furniture work in 18 days.…
2. Eighty machines can produce 4,800 identical mobiles in 6 hours. How many mobiles…
3. If 14 compositors can compose 70 pages of a book in 5 hours, how many…
4. If 2,400 sq.m. of land can be tilled by 12 workers in 10 days, how many workers…
5. Working 4 hours daily, Swati can embroid 5 sarees in 18 days. How many days will…
6. A sum of Rs. 2,500 deposited in a bank gives an interest of Rs. 100 in 6 months.…

Exercise 1.8

1. A man can complete a work in 4 days, whereas a woman can complete it in only12…
2. Two boys can finish a work in 10 days when they work together. The first boy can…
3. Three men A, B and C can complete a job in 8, 12 and 16 days respectively. A and…
4. A tap A can fill a drum in 10 minutes. A second tap B can fill in 20 minutes. A…
5. A can finish a job in 20 days and B can complete it in 30 days. They work…
6. A, B and C can do a work in 12, 24 and 8 days respectively. They all work for…
7. A tap can fill a tank in 15 minutes. Another tap can empty it in 20 minutes.…

---

Exercise 1.1

Question 1.

There are 5 oranges in a basket of 25 fruits. The percentage of oranges is ___
A. 5%

B. 25%

C. 10%

D. 20%

Answer:

Total number of fruits in basket is 25

Number of oranges in the basket is 5

∴ Percentage of oranges in the basket = 

= 

= 20 %

Option D is the correct answer.

Question 2.

2/25 = _______ %.
A. 25

B. 4

C. 8

D. 15

Answer:

Here, they asked that 2 is what percentage of 25.

= 8 %

Option C is the correct answer.

Question 3.

15% of the total number of biscuits in a bottle is 30. The total number of biscuits is _______.
A. 100

B. 200

C. 150

D. 300

Answer:

Given that 15% of the total number of biscuits in a bottle is 30.

⇒ 

Total no. of biscuits 

⇒ Total no. of biscuits = 200

(OR)

Shortcut method:

Given that 15 % = 30 biscuits

Dividing both sides with 15

1 % = 2 biscuits

Since 100% is total no. of biscuits

Multiply by 100 on both sides

100 % = 200 biscuits

∴ Total no. of biscuits = 200

Option B is the correct answer.

Question 4.

The price of a scooter was Rs. 34,000 last year. It has increased by 25% this year. Then the increase in price is _______.
A. Rs. 6,500

B. Rs. 8,500

C. Rs. 8,000

D. Rs. 7,000

Answer:

Given,

Price of scooter is Rs. 34,000 in the last year

They said that current price is increased by 25% when compared to the last year.

That means the increased price is 25% of 34,000

⇒ 

= 25 × 340

= 8500

Option B is the correct answer.

Question 5.

A man saves Rs. 3,000 per month from his total salary of Rs. 20,000. The percentage of his savings is _______ .
A. 15%

B. 5%

C. 10%

D. 20%

Answer:

Total salary of the man is 20,000 rupees

He saves 3,000 rupees per month

percentage of his savings = 

= 

= 

= 15%

Option A is the correct answer.

Question 6.

20% of the total quantity of oil is 40 liters. Find the total quantity of oil in liters.

Answer:

Given that 20% of the total quantity of oil is 40 liters.

⇒ 

Total quantity of oil 

⇒ Total quantity of oil = 200 liters

Question 7.

25% of a journey covers 5,000 km. How long is the whole journey?

Answer:

Given that 25% of total journey is 5,000 km

 = 

Total journey = 

= 5,000 × 4

= 20,000

Question 8.

3.5% of an amount is Rs. 54.25. Find the amount.

Answer:

Given that 3.5% of an amount is Rs. 54.25

Total amount = 

Total amount = 1,550

Question 9.

60% of the total time is 30 minutes. Find the total time.

Answer:

Given that 60% of an total time is 30 minutes

Total time = 

Total time = 50 minutes

Question 10.

4% sales tax on the sale of an article is Rs. 2. What is the amount of sale?

Answer:

Given that 4 % of sales tax is Rs. 2

Amount of Sale = 

= 50

∴ Amount of Sale is Rs. 50

Question 11.

Meenu spends Rs. 2000 from her salary for recreation which is 5% of her salary. What is her salary?

Answer:

Given that Meenu spends 5% of her salary which is Rs. 2000

Total Salary = 

Total Salary = 40,000

Question 12.

25% of the total mangoes which are rotten is 1,250. Find the total number of mangoes in the basket. Also, find the number of good mangoes.

Answer:

Given 1250 mangoes are rotten which is 25 % of the total

25 % = 1250 mangoes

Multiply by 4 we will get 100% which is total amount of mangoes

4 × 25 % = 4 × 1250

100 % = 5000

Total mangoes are 5000

If 25 % mangoes are rotten in a basket then (100-25) % will be good

Good mangoes (75 %) = 100% -25%

= 5000-1250

= 3750

∴ 3750 mangoes are good.

Question 13.

The marks obtained by Rani in her twelfth standard exams are tabulated below. Express these marks as percentages.

Answer:

They have given us the marks obtained and max. marks of that subject. We need to find the percentage of marks obtained in each subject.

i. ENGLISH:

Marks obtained = 180

Max. marks in English = 200

Percentage of marks scored in English = 

= 

= 90%

ii. TAMIL

Marks obtained = 188

Max. marks in Tamil = 200

Percentage of marks scored in Tamil = 

= 

= 94%

iii. Mathematics

Marks obtained = 195

Max. marks in mathematics = 200

Percentage of marks scored in mathematics = 

= 

= 97.5%

iv. Physics

Marks obtained = 132

Max. marks in Physics = 150

Percentage of marks scored in Physics = 

= 

= 88%

v. Chemistry

Marks obtained = 142

Max. marks in Chemistry = 150

Percentage of marks scored in Chemistry = 

= 

= 94.66%

vi. Biology

Marks obtained = 140

Max. marks in Biology = 150

Percentage of marks scored in Biology = 

= 

= 93.33%

Question 14.

A school cricket team played 20 matches against another school. The first school won 25% of them. How many matches did the first school win?

Answer:

Given that total 20 matches were played.

Out of that 25% of the matches are won by first school.

We should know that 25% is  of 100%

That means  of total matches gives us 25% of matches

⇒ = 5

∴ first school won 5 matches.

Question 15.

Rahim deposited Rs. 10,000 in a company which pays 18% simple interest p.a. Find the interest he gets for a period of 5 years.

Answer:

Simple interest is same as percentages

The company pays 18% simple interest for his 10,000 every year

First year -  = 1,800

In simple interest every year same interest will be paid.

So, for five years = 5 × 1,800

= 9,000

He will get Rs. 9,000 as interest for the period of 5 years.

Question 16.

The marked price of a toy is Rs. 1,200. The shop keeper gave a discount of 15%. What is the selling price of the toy?

Answer:

Given price of toy is Rs. 1,200

The shop keeper offered a discount of 15%.

So, the current price is (100-15) % of previous price

= 85% of 1,200

= 

= 1,020

After the discount of 15% the toy price is Rs. 1,020

Question 17.

In an interview for computer firm 1,500 applicants were interviewed. If 12% of them were selected, how many applicants were selected? Also find the number of applicants who were not selected.

Answer:

No. of applicants = 1,500

No. of persons selected is 12% of applicants

⇒ 

= 180

180 applicants were selected out of 1,500 applicants

If 180 selected means remaining are rejected

⇒ (1,500 – 180) are not selected

1,320 applicants were not selected.

Question 18.

An alloy consists of 30% copper and 40% zinc and the remaining is nickel. Find the amount of nickel in 20 kilograms of the alloy.

Answer:

The alloy weighs totally 20 kgs.

The alloy consists of 30% copper and 40% zinc and the remaining is nickel.

From the above we can say that 30% nickel is there in an alloy

⇒ 

⇒ 60

= 60 kg.

The amount of nickel in 20 kilograms of the alloy is 60 Kg.

Question 19.

Pandian and Thamarai contested for the election to the Panchayat committee from their village. Pandian secured 11,484 votes which was 44% of the total votes. Thamarai secured 36% of the votes. Calculate (i) the number of votes cast in the village and (ii) the number of voters who did not vote for both the contestants.

Answer:

i) Given that Pandian secured 11,484 of votes which is 44% of the total votes

⇒ 

Total votes =  = 26,100

ii) They have given that Pandian, Thamarai has got 44%, 36% of votes respectively

It clearly shows that 20% of votes was not casted

That means 

5,220 votes were not casted.

Question 20.

A man spends 40% of his income for food, 15% for clothes and 20% for house rent and saves the rest. What is the percentage of his saving? If his income is Rs. 34,400, find the amount of his savings.

Answer:

Given income of the man is Rs. 34,400

He spends 40% for food, 15% for clothes and 20% for house rent and saves the remaining of his income.

Savings = 100 – 40 – 15 – 20 = 25%

He saves 25% of his income

That means he saves ^th of his income.

⇒  = 8,600

He saves 8,600 which is 25% of his income.

Question 21.

Jyothika secured 35 marks out of 50 in English and 27 marks out of 30 in Mathematics. In which subject did she get more marks and how much?

Answer:

Given Jyothika marks in English is 35 out of 50

Which means 35 is marks secured and 50 is the max. marks

Percentage of marks in English = 

=  = 70%

Jyothika in Mathematics was 27 out of 30

Percentage of marks in Mathematics = 

=  = 90%

She scored 20% more marks in mathematics than in English.

Question 22.

A worker receives Rs. 11,250 as bonus, which is 15% of his annual salary. What is his monthly salary?

Answer:

Given that worker receives 15% of his annual salary as bonus, which is Rs. 11,250

⇒ 

Annual salary =  = 75,000

Monthly salary =  = 6,250

∴ worker get paid 6,250 monthly

Question 23.

The price of a suit is increased from Rs. 2,100 to Rs. 2,520. Find the percentage of increase.

Answer:

Original price of the suit is Rs. 2,100

Current price of the suit is Rs. 2,520

Increase in price = original Price – Previous price

= 2,520 – 2,100 = 420

Percentage increase in price = 

= 

= 20%

---

Exercise 1.2

Question 1.

Find the Cost price / Selling price.

Answer:

(i) Cost price = Rs. 7282

Profit = Rs. 208

Profit = Selling price - Cost price

Selling price = profit + cost price

= 208 + 7282 = 7490

(ii) Profit = Rs. 72

Selling price = Rs. 572

Profit = Selling price - Cost price

Cost price = Selling price – Profit

= 572 – 72 = 500

(iii) Cost price = Rs. 9684

Loss = Rs. 684

Loss = Cost Price – Selling price

Selling price = cost price - loss

= 9684 – 684 = 9,000

(iv) Profit = Rs. 273

Selling price = Rs. 1973

Profit = Selling price - Cost price

Cost price = Selling price – Profit

= 1973 – 273 = 1700

(v) Cost price = Rs. 6,76,000

Loss = Rs. 18,500

Loss = Cost Price – Selling price

Selling price = cost price - loss

= 6,76,000 – 18,500 = 6,57,500

Question 2.

Fill up the appropriate boxes and leave the rest.

Answer:

1. Cost price = 320

Selling price = 384

Since selling price < Cost price

Profit = Selling Price - Cost price

= 384 – 320 = 64

Profit % = 

= 

= 20%

2. Cost price = 2500

Selling price = 2700

Since selling price < Cost price

Profit = Selling Price - Cost price

= 2700 – 2500 = 200

Profit % = 

= 

= 8%

3. Cost price = 380

Selling price = 361

Since selling price > Cost price

Loss = Cost price - Selling Price

= 380 – 361 = 19

loss % = 

= 

= 5%

4. Cost price = 40

Loss = 2

Loss = Cost price - Selling Price

Selling Price = Cost price – Loss

= 40 – 2 = 38

loss % = 

= 

= 5%

5. Cost price = 5000

Profit = 500

Profit = Selling Price - Cost price

Selling Price = Cost price + Profit

= 5,000 – 500 = 5,500

Profit % = 

= 

= 10%

Question 3.

Find the S.P. if a profit of 5% is made on

a bicycle of Rs. 700 with Rs. 50 as overhead charges.

Answer:

Cost price of the Bicycle is 700 + 50 = 750

Profit % = 5%

Profit % = 

5 = 

 = S.P

Selling Price = 787.5

Question 4.

Find the S.P. if a profit of 5% is made on

a computer table bought at Rs. 1,150 with Rs. 50 as transportation charges.

Answer:

Cost price of computer table is 1150 + 50 = 1200

Profit % = 5%

Profit % = 

5 = 

 = S.P

Selling Price = 1,260

Question 5.

Find the S.P. if a profit of 5% is made on

a table-top wet grinder bought for Rs. 2,560 and an expense of Rs. 140 on repair charges.

Answer:

Cost price of table-top wet grinder is 2560 + 140 = 2700

Profit % = 5%

Profit % = 

5 = 

 = S.P

Selling Price = 2,835

Question 6.

By selling a table for Rs. 1,320, a trader gains 10%. Find the C.P. of the table.

Answer:

Selling Price = 1320

Profit% = 10%

Profit % = 

10 = 

C.P = 10(1320 – C.P)

11 C.P = 13200

C.P = 1,200

Question 7.

The cost price of 16 note books is equal to the selling price of 12 note books. Find the gain percent.

Answer:

Given, C.P of 16 note books is equal to the S.P of 12 note books

16 C.P = 12 S.P

C.P =  S.P

Where, C.P – Cost price

S.P – Selling Price

Gain = S.P – C.P

= S.P -  S.P

=  S.P

Profit % = 

=  × 100%

= 

= 33.33%

Question 8.

A man sold two articles at Rs. 375 each. On the first article, he gains 25% and on the other, he loses 25%. How much does he gain or lose in the whole transaction? Also, find the gain or loss percent in the whole transaction.

Answer:

Let x, y be the two articles.

Selling price of both the articles(S.P_x , S.P_y) is 375

S.P_x , S.P_y means selling price of article X, Y respectively

C.P_x , C.P_y means Cost price of article X, Y respectively

on selling article X he gets 25% profit which means the selling price is 125% of C.P_x

375 = 125% C.P_x

375 = C.P_x

C.P_x =  = 300

on selling article Y he gets 25% loss which means the selling price is 75% of C.P_y

375 = 75% C.P_y

375 = C.P_y

C.P_y =  = 500

C.P = C.P_x + C.P_y

= 300 + 500 = 800

S. P = S.P_x + S.P_y

= 375 + 375 = 750

Loss = C.P – S.P

= 800 – 750 = 50

loss % = 

= 

= 6.25%

Question 9.

Anbarasan purchased a house for Rs. 17,75,000 and spent Rs. 1,25,000 on its interior decoration the house to make a profit of 20%. Find the S.P. of the house.

Answer:

Cost price of house is 17,75,000

Interior decoration is 1,25,000

∴ total cost of house will become 17,75,000 + 1,25,000

= 19,00,000

Profit % = 20%

Profit % = 

20 = 

profit

Profit = 3,80,000

Profit = S.P - C.P

3,80,000 = S.P – 19,00,000

S.P = 22,80,000

Question 10.

After spending Rupees sixty thousand for remodeling a house, Amla sold a house at a profit of 20%. If the selling price was Rupees forty-two lakhs, how much did she spend to buy the house?

Answer:

Selling price (S.P) = 42,00,000

Spent on remodeling = 60,000

Profit % = 20%

Profit % = 

20 = 

2×C.P = 10(42,00,000 – C.P)

12 C.P = 4,20,00,000

C.P = 35,00,000

Cost Price = Cost price of house + other expenses

35,00,000 = C.P of house + 60,000

C.P of house = 34,40,000

Question 11.

Jai kumar bought a plot of land in the outskirts of the city for Rs. 21,00,000. He built a wall around it for which he spent Rs. 1,45,000. And then he wants to sell it at Rs. 25,00,000 by making an advertisement in the newspaper which costs him Rs. 5,000. Now, find his profit percent.

Answer:

Purchasing cost of the land = 21,00,000

Cost for building a wall = 1,45,000

Advertisement cost = 5,000

Total cost price of the plot = 21,00,000 + 1,45,000 + 5,000

= 22,50,000

Selling price = 25,00,000

Profit = Selling price - cost price

= 25,00,000 – 22,50,000 = 2,50,000

Profit % = 

= × 100%

= 11.11%

Question 12.

A man sold two varieties of his dog for Rs. 3,605 each. On one he made a gain of 15% and on the other a loss of 9%. Find his overall gain or loss.

[Hint: Find C.P. of each]

Answer:

Let x, y be the two varieties of dogs.

Selling price of both the varieties (S.P_x , S.P_y) is 3605

S.P_x , S.P_y means selling price of varieties X, Y respectively

C.P_x , C.P_y means Cost price of varieties X, Y respectively

on selling variety X dog he gets 15% profit which means the selling price is 115% of C.P_x

3605 = 115% C.P_x

3605 = C.P_x

C.P_x =  = 3134.78

on selling variety Y dog he gets 9% loss which means the selling price is 91% of C.P_y

3605 = 91% C.P_y

3605 = C.P_y

C.P_y =  = 3,961.53

C.P = C.P_x + C.P_y

= 3134.78 + 3,961.53 = 7096 (approx.)

S. P = S.P_x + S.P_y

= 3605 + 3605 = 7,210

Profit = S.P - C.P

= 7,210 – 7,096 = 114 (approx.)

---

Exercise 1.3

Question 1.

The discount is always on the _______.
A. Marked Price

B. Cost Price

C. Selling Price

D. Interest

Answer:

Discount is always given on the marked price of the product.

Selling price is the Discount on marked price.

Option A is the correct answer.

Question 2.

If M.P. = Rs. 140, S.P. = Rs. 105, then Discount = _______.
A.Rs. 245

B.Rs. 25

C.Rs. 30

D.Rs. 35

Answer:

Selling price is the Discount on marked price.

Marked price = Selling price + Discount.

Discount = Marked price - Selling price

= 140 – 105 = 35

Option D is the correct answer.

Question 3.

______ = Marked Price – Discount.
A. Cost Price

B. Selling Price

C. List Price

D. Market price

Answer:

Selling price is the Discount on marked price.

Marked price = Selling price + Discount.

Selling price = Marked Price – Discount

Option B is the correct answer.

Question 4.

The tax added to the value of the product is called ______ Tax.
A. Sales Tax

B. VAT

C. Excise Tax

D. Service Tax

Answer:

It is called VAT

VAT means value added tax

Option B is the correct answer.

Question 5.

If the S.P. of an article is Rs. 240 and the discount given on it is Rs. 28, then the M.P. is _______.
A.Rs. 212

B.Rs. 228

C.Rs. 268

D.Rs. 258

Answer:

S.P = 240

Discount = 28

Marked price = Selling price + Discount.

= 240 + 28 = 268

Option C is the correct answer.

Question 6.

The price marked on a book is Rs. 450. The shopkeeper gives 20% discount on it a in book exhibition. What is the Selling Price?

Answer:

Marked price = 450

Discount = 20% of M.P

=  = 90

Selling price = Marked Price – Discount

= 450 – 90 = 360

Question 7.

A television set was sold for Rs. 5,760 after giving successive discounts of 10% and 20% respectively. What was the Marked Price?

Answer:

Selling price of TV = 5,760

They have given successive discounts of 10% and 20% respectively

Selling price given is after the 2 discounts as mentioned.

Let x be the marked price of TV

So, selling price after 10% discount = x -  x = 0.9x

selling price after 20% discount = 0.9x -  = 0.9x (1-0.2)

5,760 = (0.9) (0.8)x

x = 

= 8,000

∴ 8,000 is the marked price of TV.

Question 8.

Sekar bought a computer for Rs. 38,000 and a printer for Rs. 8,000. If the rate of sales tax is 7% for these items, find the price he has to pay to buy these two items.

Answer:

Cost price of computer and printer are 38,000 and 8,000 respectively

∴ cost price is 38,000 + 8,000 = 46,000

Rate of sales tax is 7%

sales tax = (rate of sales tax) (cost of the product)

= 7% (46,000)

=  (46,000) = 3,220

∴ 3,220 is the sales tax amount for computer and printer

∴ Total cost to be paid for both computer and printer is

46,000 + 3,220 = 49,220

Question 9.

The selling price with VAT, on a cooking range is Rs. 19,610. If the VAT is 6%, what is the original price of the cooking range?

Answer:

Given

Selling price with VAT = 19,610

VAT is 6%

Let y be cost of cooking range

VAT amount = (VAT)(cost of cooking range)

= 6%(y)

= y = 0.06y

Selling price = cost of the cooking range + VAT amount

19,610 = y + 0.06 y

19,610 = 1.06 y

 = y

y = 18,500

original price of the cooking range = 18,500

Question 10.

Richard got a discount of 10% on the suit he bought. The marked price was Rs. 5,000 for the suit. If he had to pay sales tax of 10% on the price at which he bought, how much did he pay?

Answer:

The marked price of the suit is 5,000

Discount offered is 10% of marked price

=  × 5,000 = 500

Selling price = marked price - Discount

= 5,000 – 500 = 4,500

∴ He bought the suit for 4,500

He need to pay 10% as sales tax

Amount of sales tax = (rate of tax) (cost of the item)

= 10% ( 4,500)

=  × 4,500

= 450

∴ He need to pay 450 as sales tax

Purchase price of the suit = 4,500 + 450 = 4,950

Question 11.

The sales tax on a refrigerator at the rate of 9% is Rs. 1,170. Find the actual sale price.

Answer:

Amount of sales tax is 1,170

Rate of sales tax is 9%

Let x be the cost price of refrigerator

Amount of sales tax = (Rate of sales tax) (cost price)

1,170 = 9% (x)

1,170 =  x

 = x

x = 13,000

Actual cost price of refrigerator is 13,000

selling price = cost price + sales tax

= 13,000 + 1,170

= 14,170

Question 12.

A trader marks his goods 40% above the cost price. He sells them at a discount of 5. What is his loss or gain percentage?

Answer:

Let x be the cost price of the goods

Marked price is 40% above the cost price.

M.P = 40% of C.P + C.P

= 0.4x + x

= 1.4x

Discount = 5% of marked price

=  × 1.4x

= (0.05) × (1.4x)

= 0.07x

Marked price = discount + selling price

1.4x = 0.07x + S.P

S.P = 1.4x – 0.07x

= 1.33x

Profit = S.P - C.P

= 1.33x – x

= 0.33 x

Profit % = 

=  × 100%

= 33 %

Question 13.

A T.V. with marked price Rs. 11,500 is sold at 10% discount. Due to festival season, the shop keeper allows a further discount of 5%. Find the net selling price of the T.V.

Answer:

Marked price of TV is 11,500

He has given 2 discounts,

Discount of 10% = 

= 1,150

Selling price after first discount = marked price – discount of 10%

= 11,500 -1,150

= 10,350

Now 11,350 will becomes as the marked price

Discount of 5% due to festive season

Discount =  × 10,350

= 0.05 × 10,350

= 517.5

Selling price after second discount = marked price – discount of 5%

= 10,350 – 517.5

= 9,832.5

Net selling price after two discounts is 9,832.5

Question 14.

A person pays Rs. 2,800 for a cooler listed at Rs. 3,500. Find the discount percent offered.

Answer:

Marked price = 3,500

Selling price = 2,800

Discount = marked price – selling price

= 3,500 – 2,800

= 700

Discount % = 

= 

=  %

= 20%

20% is the discount offered.

Question 15.

Deepa purchased 15 shirts at the rate of Rs. 1,200 each and sold them at a profit of 5%. If the customer has to pay sales tax at the rate of 4%, how much will one shirt cost to the customer?

Answer:

Cost of each shirt = 1,200

No. of shirts = 15

Cost price of shirts = 15 × 1,200 = 18,000

Profit = 5%

=  × 18,000

= 900

Total cost price = 18,000 + 900 = 18,900

Sales Tax = 4%

Amount of sales tax = (Rate of sales tax) (cost price)

=  × 18,900

= 756

Total cost that customer has to pay = cost price + sales tax amount

= 18,900 + 756

= 19,656

Cost of 15 shirt that customer pay = 19,656

Cost of 1 shirt that customer has to pay =  = 1,310.40

Question 16.

Find the discount, discount percent, selling price and the marked price.

Answer:

(i) Saree

Marked price = 2,300

Discount% = 20%

Discount = 20% of marked price

=  × 2,300 = 460

Selling price = Marked price – Discount

= 2,300 - 460 = 1,840

(ii) Pen set

Marked price = 140

Selling price = 105

Discount = Marked price – Selling price

= 140 – 105 = 35

Discount % = 

= 

=  = 25%

(iii) Dining table

Discount% = 20%

Let M be the marked price

Discount =  × M = 0.2M

Selling price = 16,000

Marked price = selling price + discount

M = 16,000 + 0.2M

0.8M = 16,000

M = 

= 20,000

Discount = Marked price - selling price

= 20,000 – 16,000

= 4,000

(iv) Washing machine

Marked price = 14,500

Selling price = 13,775

Discount = Marked price – Selling price

= 14,500 – 13,775 = 725

Discount % = 

= 

=  = 5%

(v) Crockery set

Marked price = 3,224

Discount% = 12.5%

Discount = 12.5% of marked price

=  × 3,224 = 403

Selling price = Marked price – Discount

= 3,224 - 403 = 2,821

---

Exercise 1.4

Question 1.

Find the Amount and Compound Interest in the following cases:

Answer:

Amount = 

P is the principle

r is the rate of interest

n is the time period in terms of years

(i) Principle = 1000

Rate of interest per annum = 5%

Time = 3 years

Amount = 

= 

= 1,157.625

Compound Interest = Amount – Principle

= 1000 – 1,157.625

= 157.625

(ii) Principle = 4000

Rate of interest per annum = 10%

Time = 2 years

Amount = 

= 

= 4,840

Compound Interest = Amount – Principle

= 4000 – 4,840

= 840

(iii) Principle = 18,000

Rate of interest per annum = 10%

Time =  years

We are going to find the compound interest year by year

For 1^st year

Amount = 

= 

= 19,800

Now 19,800 become the principle amount

For 2^nd year

Amount = 

= 

= 21,780

Amount = 

P is the principle

r is the rate of interest

n is the time period in terms of years

For half yearly

Amount = 

= 

= 22,869

Compound Interest = Amount – Principle

= 22,869 – 18,000

= 4,869

Question 2.

Sangeetha borrowed Rs. 8,000 from Alex for 2 years at 121/2% per annum. What interest did Sangeetha pay to Alex if the interest is compounded annually?

Answer:

Rate of interest – 12.5% P.A

Principle – 8,000

Time – 2 years

Amount = 

= 

= 10,125

Compound interest = Amount – principle

= 10,125 – 8,000 = 2,125

Question 3.

Maria invested Rs. 80,000 in a business. She would be paid interest at 5% per annum compounded annually. Find

(i) the amount standing to her credit at the end of second year and (ii) the interest for the third year.

Answer:

i. Principle = 80,000

Rate of interest per annum = 5%

Time =  years

Compound interest for 2 years

Amount = 

= 

= 88,200

Compound interest = Amount – principle

= 80,000 - 88,200 = 8,200

8,200 will be credited at the end of 2 years

ii. Compound interest for 3 years

Amount = 

= 

= 92,610

Compound interest = Amount – principle

= 80,000 – 92,610 = 12,610

Compound interest for 3^rd year

= compound interest of 3 years – compound interest of 2 years

= 12,610 - 8,200

= 4,410

Compound interest for the 3^rd year is 4,410

Question 4.

Find the compound interest on Rs. 24,000 compounded half - yearly for 11/2 years at the rate of 10% per annum.

Answer:

Principle = 24,000

Rate of interest per annum = 10%

Time = 1.5 years

Amount = 

= 

= 27,783

Compound interest = Amount – principle

= 24,000 – 27,783

= 3,783

Question 5.

Find the amount that Dravid would receive if he invests Rs. 8,192 for 18 months at 121/2% per annum, the interest being compounded half - yearly.

Answer:

Principle = 8,192

Time = 18 months

Rate = 12.5 P.A

Amount = 

= 

= 9,826

Question 6.

Find the compound interest on Rs. 15,625 for 9 months, at 16% per annum compounded quarterly.

Answer:

Principle = 15,625

Rate of interest = 16%

Time = 9 months

Amount = 

= 

= 17,576

Compound interest = amount – principle

= 17,576 – 15,625

= 1,951

Question 7.

Find the Principle that will yield a compound interest of Rs. 1,632 in 2 years at 4% rate of interest per annum.

Answer:

Let x be the principle

Rate of interest = 4%

Time = 2 years

Compound interest = 1,632

Amount = x 

= x

= 1.0816x

Compound interest = amount – principle

1,632 = 1.0816x – x

 = x

X = 20,000

∴ principle is 20,000

Question 8.

Vicky borrowed Rs. 26,400 from a bank to buy a scooter at the rate of 15% p.a. compounded yearly. What amount will he pay at the end of 2 years and 4 months to clear the loan?

Answer:

Capital = 26,400

Rate of interest = 15%

Time = 2 years

Amount = 

= 

= 36,659.7

Question 9.

Arif took a loan of Rs. 80,000 from a bank. If the rate of interest is 10% p. a., find the difference in amounts he would be paying after 11/2 years if the interest is

(i) compounded annually and

(ii) compounded half - yearly.

Answer:

Capital = 80,000

Rate of interest = 10%

Time = 1 years

i. Amount = 

= 

= 92,400

ii. Amount = 

= 

= 92,610

Question 10.

Find the difference between simple interest and compound interest on Rs. 2,400 at 2 years at 5% per annum compounded annually.

Answer:

Principle – 2,400

Interest – 5%

Time – 2 years

Compound interest

Amount = 24,000 

= 24,00 

= 2,646

Compound interest = amount – principle

= 2,646 – 2,400 = 246

Simple interest = 

= 

= 240

The difference between compound and simple interest = 246 -240

= 6

Question 11.

Find the difference between simple interest and compound interest on Rs. 6,400 for 2 years at 6 1/4% p. a. compounded annually.

Answer:

Capital = 6,400

Rate of interest = 6.25%

Time = 2years

Compound interest

Amount = 6,400 

= 6,400 

= 7,225

Compound interest = amount – principle

= 7,225 – 6,400 = 825

Simple interest = 

= 

= 800

The difference between compound and simple interest = 825 - 800

= 25

Question 12.

The difference between C. I. and S. I. for 2 years on a sum of money lent at 5% p.a. is Rs. 5. Find the sum of money lent.

Answer:

Let x be the sum of money lent

Time = 2 years

Interest = 5%

C.I – S.I = 5

Amount = x 

= x

= 1.1025x

C.I = amount – principle

= 1.1025x – x

= 0.1025x

Simple interest = 

= 

= 0.1x

C.I – S.I = 5

0.1025x – 0.1x = 5

0.0025x = 5

X = 2,000

∴ sum of money lent is 2,000

Question 13.

Sujatha borrows Rs. 12,500 at 12% per annum for 3 years at simple interest and Radhika borrows the same amount for the same period at 10% per annum compounded annually. Who pays more interest and by how much?

Answer:

sujatha

Principle = 12,500

Interest = 12%

Time = 3 years

Simple interest = 

= 

= 4,500

Radhika

Principle = 12,500

Interest = 10%

Time = 3 years

Amount = 

= 

= 16,637.5

Compound interest = Amount – principle

= 16,637.5 – 12,500

= 4,137.5

∴ Sujatha pays 362.5 more than Radhika

Question 14.

What sum is invested for 11/2 years at the rate of 4% p.a. compounded half –yearly which amounts to Rs. 1,32,651?

Answer:

Interest = 4%

Time = 1.5 years =  years

Amount = 1,32,651

Sum = ?

Let x be the sum of amount

Amount = 

1,32,651 = 

1,32,651 = 1.061208x

x = 

x = 1,25,000

∴ The principle amount is 1,25,000

Question 15.

Gayathri invested a sum of Rs. 12,000 at 5% p.a. at compound interest. She received amount of Rs. 13,230 after ‘n’ years. Find the value of ‘n’.

Answer:

Sum of money invested = 12,000

Rate of interest = 5%

Amount = 13,230

Amount = 

13,230 = 

1.1025 = 

Taking log on bo21th sides

 = n 

 = n

N = 2 years

Question 16.

At what rate percent compound interest per annum will Rs. 640 amounts to Rs. 774.40 in 2 years?

Answer:

Principle = 640

Amount = 774.40

Time = 2 years

Interest rate = ?

Let interest rate be x

Amount = 

774.40 = 

 – 100 = x

X = 10

∴ interest rate is 10%

Question 17.

Find the rate percent per annum, if Rs. 2,000 amounts to Rs. 2,315.25 in an year and a half, interest being compounded half-yearly.

Answer:

Principle = 2,000

Amount = 2,315.25

Time = 1.5 year

Interest rate = ?

Let interest rate be x

Amount = 2,000 

2,315.25 = 2,000

 – 200 = x

X = 10

∴ interest rate is 10%

---

Exercise 1.5

Question 1.

The number of students enrolled in a school is 2000. If the enrolment increases by 5% every year, how many students will be there after two years?

Answer:

Number of students in school = 2,000

Rate of increasing = 5%

For 1^st year

No. of students enrolled in the 1^st year = 5% of 2,000

= 

= 100

After 1-year no. of students in the school is 2100

For 2^nd years

No. of students enrolled in the 2^nd year = 5% of 2,100

= 

= 105

After 2-year no. of students in the school is 2205

Question 2.

A car which costs Rs. 3,50,000 depreciates by 10% every year. What will be the worth of the car after three years?

Answer:

Current worth of car(P) = 3,50,000

Rate of depreciation(R) = 10%

No. of years(n) = 3

The worth of car after 3 years = 

= 

= 2,55,150

The worth of car after 3 years is 2,55,150

Question 3.

A motorcycle was bought at Rs. 50,000. The value depreciated at the rate of 8% per annum. Find the value after one year.

Answer:

Motor cycle price (P) = 50,000

Rate of depreciation(R) = 8%

No. of years(n) = 1

The worth of motor cycle after 1 year = 

= 

= 500 (92)

= 46,000

The worth of motor cycle after 1 year is 46,000

Question 4.

In a Laboratory, the count of bacteria in a certain experiment was increasing at the rate of 2.5% per hour. Find the bacteria at the end of 2 hours if the count was initially 5,06,000.

Answer:

Initial count (P) = 5,06,000

Rate of increase (R) = 2.5% per hour

No. of hours(n) = 2

The count of bacteria after 2 hours = 

= 

= 5060 × 102.5²

= 5,31,61,625

Question 5.

From a village people started migrating to nearby cities due to unemployment problem. The population of the village two years ago was 6,000. The migration is taking place at the rate of 5% per annum. Find the present population.

Answer:

Population before 2 years (P) = 6,000

Rate of migration (R) = 5%

No. of years (n) = 2

Present population = 

= 6,000 × 

= 0.6 (95)²

= 5,415

Present population in the village is 5,415

Question 6.

The present value of an oil engine is Rs. 14,580. What was the worth of the engine 3 years before if the value depreciates at the rate of 10% every year?

Answer:

present value of an oil engine = 14,580.

Rate of depreciation(R) = 10%

No. of years(n) = 3

Value of engine oil before 3 years (P) = ?

present value of an oil engine = 

14,580 = 

14,580 = 

P = 

P = 20,000

Value of engine oil before 3 years (P) is 20,000

Question 7.

The population of a village increases by 9% every year which is due to the job opportunities available in that village. If the present population of the village is11,881, what was the population two years ago?

Answer:

Current population of village = 11,881

Rate of increase (R) = 9%

No. years (n) = 2

Population of the village before 2 years (P) = ?

Current population of village = 

11,881 = 

P = 

P = 10,000

Population of the village before 2 years (P) = 10,000

---

Exercise 1.6

Question 1.

Ponmani makes a fixed deposit of Rs. 25,000 in a bank for 2 years. If the rate of interest is 4% per annum, find the maturity value.

Answer:

Total deposit (p) = 25,000

No. of years (N) = 2 years

Rate of interest (R) = 4% per annum

Interest = p× N × 

= 25,000 × 2 × 

= 2,000

Maturity value = Total deposit + Interest

= 25,000 + 2,000

= 27,000

Question 2.

Deva makes a fixed deposit of Rs. 75,000 in a bank for 3 years. If the rate of interest is 5% per annum, find the maturity value.

Answer:

Total deposit (p) = 75,000

No. of years (N) = 3 years

Rate of interest (R) = 5% per annum

Interest = p× N × 

= 75,000 × 3 × 

= 11,250

Maturity value = Total deposit + Interest

= 75,000 + 11,250

= 86,250

Question 3.

Imran deposits Rs. 400 per month in a post office as R.D. for 2 years. If the rate of interest is 12%, find the amount he will receive at the end of 2 years.

Answer:

Amount deposited (P) = 400/ month

No. of years (n) = 2 years = 2 × 12 = 24 months

Rate of interest (R) = 12%

Total deposit made = P × n

= 400 × 24 = 9,600

Period for recurring deposit, (N) = 

=  = 25 years

Interest = p× N × 

= 400 × 25 × 

= 1,200

Maturity amount = P × n + p× N × 

= 9,600 + 1,200

= 10,800

He will receive 10,800 at the end of 2 years

Question 4.

The cost of a microwave oven is Rs. 6,000. Poorani wants to buy it in 5 instalments. If the company offers it at the rate of 10% p. a. Simple Interest, find the E.M.I. and the total amount paid by her.

Answer:

Cost of microwave (P) = 6,000

Rate of interest (R) = 10%

No. of installments (N) = 5 months = years

Interest = p× N × 

= 6,000 ×× 

= 250

Total amount to be paid for microwave oven = 6000 + 250

= 6250

Amount to be paid on every installment =  = 1,250

Question 5.

The cost price of a refrigerator is Rs. 16,800. Ranjith wants to buy the refrigerator at 0% finance scheme paying 3 E.M.I. in advance. A processing fee of 3% is also collected from Ranjith. Find the E.M.I. and the total amount paid by him for a period of 24 months.

Answer:

cost price of a refrigerator (P) Rs. 16,800

No. of months (N) = 24

Interest = 0%

Processing Fess = 3%

E.M.I = 

= 

= 700

Given that 3 EMI are paid in advance

= 700 × 3

= 2,100

Processing fess is 3% of cost price

=  × 16,800 = 504

Total amount to be paid = Initial payment + processing fees + cost

price

= 2,100 + 504 + 16,800

= 19,404

Question 6.

The cost of a dining table is Rs. 8,400. Venkat wants to buy it in 10 instalments. If the company offers it for a S.I. of 5% p. a., find the E.M.I. and the total amount paid by him.

Answer:

Cost price of dining table = 8,400

No. of installments = 10

So, n =  years

Rate of Interest = 5%

Interest = p× N × 

=  × 8,400 × 

= 350

Total amount to be paid = interest + cost price

= 350 + 8,400

= 8,750

E.M.I = 

= 

= 875

---

Exercise 1.7

Question 1.

Twelve carpenters working 10 hours a day complete a furniture work in 18 days. How long would it take for 15 carpenters working for 6 hours per day to complete the same piece of work?

Answer:

Let x be the no. of days to be found out

Step :1

Considering the carpenter and the no. of days

The multiplying factor = 

Step :2

Considering the no. of hours in a day and the no. of days

The multiplying factor = 

x =  ×  × 18

x = 24 days

Question 2.

Eighty machines can produce 4,800 identical mobiles in 6 hours. How many mobiles can one machine produce in one hour? How many mobiles would 25 machines produce in 5 hours?

Answer:

In 6 hours, 80 machines can produce 4,800 mobiles

In 1 hour, 1 machine can produce 

= 10 mobiles

In 5 hours, 25 machines can produce = 10 × 5 × 25

= 1,250 mobiles

Question 3.

If 14 compositors can compose 70 pages of a book in 5 hours, how many compositors will compose 100 pages of this book in 10 hours?

Answer:

Step :1

Considering the No. of compositors and no. of pages

The multiplying factors 

Step :2

Considering the No. of compositors and no. of hours

The multiplying factors 

So, the No. of compositors required

x =  ×  × 14

x = 10

Question 4.

If 2,400 sq.m. of land can be tilled by 12 workers in 10 days, how many workers are needed to till 5,400 sq.m. of land in 18 days?

Answer:

Considering the Area of land and no. of workers

The multiplying factors 

Considering the No. of days and no. of workers

The multiplying factors 

So, the No. of compositors required

x =  × × 12

x = 15

Question 5.

Working 4 hours daily, Swati can embroid 5 sarees in 18 days. How many days will it take for her to embroid 10 sarees working 6 hours daily?

Answer:

Working 4 hours daily, Swati can embroid 5 sarees in 18 days

She works 4 hours in a day (here, 1 day = 4 hour)

Swati can embroid 5 sarees in 18 × 4 hour

= 72 hours

Swati can embroid 1 saree in  hours

= 14.4 hours

Time taken for embroid is 14.4 hrs/saree

Time taken for 10 sarees = 14.4hrs/saree × 10 saree

= 144 hrs

If she work 6 hours a day (here, 1 day = 6 hours)

Time taken for 10 sarees = days

= 24 days

Question 6.

A sum of Rs. 2,500 deposited in a bank gives an interest of Rs. 100 in 6 months. What will be the interest on Rs. 3,200 for 9 months at the same rate of interest?

Answer:

Considering the Sum of Amount and Interest Amount

The multiplying factors 

Considering the No. of month and no. of workers

The multiplying factors 

So, the No. of compositors required

x =  × × 100

x = 192

---

Exercise 1.8

Question 1.

A man can complete a work in 4 days, whereas a woman can complete it in only12 days. If they work together, in how many days, can the work be completed?

Answer:

A man can complete a work in 4 days

Man’s 1-day work = 

Woman can complete a work in 12 days

Woman’s 1-day work = 

1-day work of both =  +  = 

By working together, they can complete a work in 3 days

Question 2.

Two boys can finish a work in 10 days when they work together. The first boy can do it alone in 15 days. Find in how many days will the second boy do it all himself?

Answer:

If two boys work together they can finish a work in 10 days

Let the two boys be x & y

x & y’s 1-day work = 

x + y =  ..eq (1)

first boy (x) can do it in 15 days

x’s 1-day work = 

x = 

substituting the value of x in eq(1)

x + y = 

 + y = 

y = 

y’s 1-day work = 

so, second boy (y) can do a work in 30 days

Question 3.

Three men A, B and C can complete a job in 8, 12 and 16 days respectively.

A and B work together for 3 days; then B leaves and C joins. In how many days, can A and C finish the work?

Answer:

A, B and C can complete a job in 8, 12 and 16 days respectively.

1-Day work:

A’s = 

B’s = 

C’s = 

A and B’s 1-day work =  +  = 

A and B work together for 3 days

= 3 ×  = 

The remaining work after 3 days = 1- = 

The remaining work will be done by A & C together

Work done by A & C = 

By doing  potion of the work in a day they can complete remaining work () in 2 days

Question 4.

A tap A can fill a drum in 10 minutes. A second tap B can fill in 20 minutes. A third tap C can empty in 15 minutes. If initially the drum is empty, find when it will be full if all taps are opened together?

Answer:

Time taken by A = 10 min

Work done by A in 1 min = 

Time taken by B = 20 min

Work done by B in 1 min = 

Time taken by C = 15 min

Work done by C in 1 min = 

Work done by all three A, B & C in 1 min =  +  -  = 

Time taken by all three A, B & C in = 12 min

Question 5.

A can finish a job in 20 days and B can complete it in 30 days. They work together and finish the job. If Rs. 600 is paid as wages, find the share of each.

Answer:

Time taken by A = 20 days

Work done by A in 1 day = 

Time taken by B = 30 days

Work done by B in 1 day = 

Wages = 600

Ratio of work done by A & B in 1-day =  :  = 3:2

So. The ratio of the wages will be 3:2

3x + 2x = 600

5x = 600

X = 120

A’s wage = 3x = 3 × 120 = 360

B’s wage = 2x = 2 × 120 = 240

Question 6.

A, B and C can do a work in 12, 24 and 8 days respectively. They all work for one day. Then C leaves the group. In how many days will A and B complete the rest of the work?

Answer:

A, B and C can do a work in 12, 24 and 8 days respectively.

A, B and C’s 1-day work will be  ,  , respectively

1-day’s work of all of them =  +  +  = 

Remaining portion of work = 1-  = 

After that C leaves the group. So, the rest of the work will be completed by A & B only

A & B’s 1-day’s work =  + = 

No. of day required =  =  = 6 days

Question 7.

A tap can fill a tank in 15 minutes. Another tap can empty it in 20 minutes. Initially the tank is empty. If both the taps start functioning, when will the tank become full?

Answer:

Time taken by A = 15 min

Work done by A in 1 min = 

Time taken by B = 30 min

Work done by B in 1 min = 

Work done by all three A, B in 1 min =  -  = 

(∵ B empties the tank we use negative there)

Time taken to fill to the tank is 60 min