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### Priya earned 15,000 in the first month. Thereafter her salary increased by 1500 per year. Her expenses are 13,000 during the first year and the expenses increases by 900 per year. How long will it take for her to save 20,000 per month.

Priya earned 15,000 in the first month. Thereafter her salary increased by 1500 per year. Her expenses are 13,000 during the first year and the expenses increases by 900 per year. How long will it take for her to save 20,000 per month.

Solution :

Increment of salary per year = 1500

monthly increment = 1500/12 = 125

write the expenses as a sequence

1st month expense = 13000

increasing expenses per year = 900

monthly increment of expenses = 900/12 = 75

Let us write the monthly earnings and expenses as a sequence.

15000, 15125, 15250,................

13000, 13075, 13150,...........

By subtract these two sequences, we get saving of each month

2000, 2050, 2100,................

From the above sequence, we may find that saving is increased 50 per month.

To get in which month will she save 20000, we have to use the formula

n = [(l - a)/d] + 1

= [(20000 - 2000)/50] + 1

n = 361 (number of months)

In 361 months, she will save 20000 per month. But we have to find the answer in years.

= 361/12 = 30.8

Hence the required number of years is 31.