Ratio, Proportion and Partnership

Ex. No. 1

1. The ratio of number of boys and girls in a school is 3:2. If 20% of the boys and 30% of the girls are scholarship holders, find the percentage of students who are not scholarship holders.

2. If the numerator of a fraction is increased by 20% and its denominator be diminished by 10%, the value of the fraction is 16/21, find the original fraction.

3. The ratio of incomes of Salim and Jawed was 20:11. Three years later income of Salim has increased by 20% and income of Jawed was increased by Rs. 500. Now ratio of their incomes becomes 3:2. Find original incomes of Salim and Jawed.

4.   In a class, 605 students are boys and 40% are girls. By admitting 16 boys and 8 girls the ratio of boys to girls becomes 8:5. What must be the number of boys and number of girls originally in the class?

5. Incomes of Mr. Shah, Mr. Patel and Mr. Mehta are in the ratio 1:2:3; while their expenditure are in the ratio 2:3:4. If Mr. Shah saves 20% of his income, find the ratio of their savings.

6.  What must be subtracted from each of the numbers 5, 7 and 10, so that the resulting numbers are in the continued proportion?

7.  The employees of a firm have maintained their standard of living in such a manner, that they all have identical percentage of saving from their salaries. Amina and Sabina are two employees of the firm. Amina spends Rs. 12,800 per month from her salary of Rs. 35,000 per month. What would be Sabina's savings per month from her salary of Rs. 48,000 per month?

8.   A certain job can be performed by 10 men in 24 days working 8 hours a day, How may days would be needed to perform the same job by 8 men working 12 hours a day?

9.  Two metals X and Y are to be used for making two different alloys. If the ratio by weight of X:Y in the first alloy is 6:5 and that in the second is 7:13. How many kg of X metal must be melted along with 11 kg of the first alloy and 20 kg of second alloy so as to produce a new alloy containing 40% of metal Y?

10.Three persons A, B and C whose salaries together amount to Rs. 21,000. Their savings are 20%, 30% and 40% of their salaries respectively. If their expenditures are in the ratio 8:14:3, find their respective salaries.

Ex. No. 2

1.       Ajay, Atul and Anil started a business in a partnership by increasing Rs. 12,000, Rs. 18,000 and Rs. 30,000 respectively. At the end of the year, they earned a profit of Rs. 15,200 in the business. Find the share of each in the profit.

2.       Raghu, Madhu and Ramu started a business in a partnership by investing Rs. 60,000, Rs. 40,000 and Rs. 75,000 respectively. At the end of the year they found that they have incurred a loss of Rs. 24,500. Find how much loss each one had to bear.

3.       A, B and C are in the partnership. A's capital was Rs. 65,000 and C's capital was Rs. 50,000. The total profit is Rs. 38,000; out of which B's profit was Rs. 15,000. What was B's capital?

4.       Paul and Qasim started a business with equal amount of capital. After 8 months Paul withdrew his amount and Raja entered in the business with same of capital. At the end of the year they found that they have incurred a loss of Rs. 24, 500. Find how much loss each one had to bear.

5.       Amit and Rohit started a business by investing Rs. 20,000 each. After 3 months Amit withdrew Rs. 5000 and Rohit put in the same amount additionally. How should a profit of Rs. 12,800 be divided between them at the end of the year?

6.        John and Mathew started a business with their capitals in the ratio 8:5. After 8 months John added 25% of his earlier capital as further investments. At the same time Mathew withdrew 20% of his earlier capital. At the end of the year they earned Rs. 52000 as profit. How should they divide it between them?

7. Ramesh, Vivek and Sunil started a business by investing the capitals in the ratio 4:5:6. After 3 months Vivek removed all his capital and after 6 months Sunil removed all his capital from the business. At the end of the year Ramesh received Rs. 6400 as profit. Find the profit earned by Vivek and Sunil.

8. Mr. Natarajan and Mr. Gopalan are partners in a company having capitals in the ratio 4:5 and profits received by them are in the ratio 5:4. If Gopalan invested capital in the company for 16 months, how long was Natrajan’s investment in the company?

9. Anita and Nameeta are partners in the business for some years. Their capitals are Rs. 3,00,000 and Rs. 2,00,000 respectively. Yogeeta wants to join the business with the capital of Rs. 4,00,000. They agree that the goodwill will be considered as two times the average of last three years profit. The profit of last three years are Rs. 60,000, Rs. 70,000 and Rs. 50,000 respectively. What are the amounts to tbe paid by Yogeeta and Anita and Nameeta as goodwill?

10. A, B and C are three partners with their capitals in the ratio 4:3:3. They decide to dissolve the partnership. The assets of the company are sold for Rs. 4,00,000 and liabilities (other than capital) of Rs. 60,000. They incur realisation expenses of Rs. 4,000. What is the amount that each partner gets as final settlement after dissolution?