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Rajiv gets an increment of 25% every year in his salary, with the increase in salary his expenditure also increases by 10% every year. In the present year Rajiv saves Rs. 99825. What was his savings 3 years back if the savings and expenditure is equal this year and an additional Rs. 350 is kept for donation this year?

Rajiv gets an increment of 25% every year in his salary, with the increase in salary his expenditure also increases by 10% every year. In the present year Rajiv saves Rs. 99825. What was his savings 3 years back if the savings and expenditure is equal this year and an additional Rs. 350 is kept for donation this year? Correct Answer Rs. 27400

Given:

Salary increases by 25% every year

Expenditure increases by 10% every year

Expenditure is equal to savings in the present year that is Rs. 99825

Rs. 350 kept for donation other than savings and expenditure

Concept:

Salary is the sum of expenditure and savings and donations

Formula:

F = S(1 + i/100)n

Where, F = final amount after n years, S = present amount, i = increment percent, n = number of years

Savings = income – expenditure

Calculation:

Let salary 3 years back was x

Present salary = x(1 + 25/100)3

Let expenditure 3 years back was y

Present expenditure = y(1 + 10/100)3

y(1 + 10/100)3 = 99825

⇒ y(110/100)3 = 99825

⇒ y(11/10)3 = 99825

⇒ 1.331y = 99825

⇒ y = 75000

Present salary = Rs. (99825 + 99825 + 350) = Rs. 200000

x(1 + 25/100)3 = 200000

⇒ x(125/100)3 = 200000

⇒ x × 1.253 = 200000

⇒ x = 102400

Savings 3 years back = Rs. (102400 – 75000) = Rs. 27400

∴ Savings 3 years back is Rs. 27400

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