Q2 of 36 Page 161

A man saved Rs 66000 in 20 years. In each succeeding year after the first year he saved Rs 200 more than what he saved in the previous year. How much did he save in the first year?

The total amount saved in 20 years is 66000 hence S20 = 66000


Let the amount saved in first year be ‘a’


Then as he increases 200rs every year then the amount in second year will be ‘a + 200’ then in third year ‘a + 400’ and so on


The sequence will be a, a + 200, a + 400…


The sequence is AP and the common difference is d = 200


There are 20 terms in the sequence as he saved money for 20 years


Using the sum formula for AP


Where n is number of terms a is the first term and d is the common difference


Given that S20 = 66000



⇒ 66000 = 10(2a + 19 × 200)


⇒ 6600 = 2a + 3800


⇒ 6600 – 3800 = 2a


⇒ 2a = 2800


⇒ a = 1400


Hence amount saved in first year is 1400 Rs.


More from this chapter

All 36 →
1

The first term of an A.P.is a, and the sum of the first p terms is zero, show that the sum of its next q terms is

[Hint: Required sum = Sp+q – Sp]


 3

A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter.

(a) Find his salary for the tenth month


(b) What is his total earnings during the first year?


 4

If the pth and qth terms of a G.P. are q and p respectively, show that its (p + q)th term is

5

A carpenter was hired to build 192 window frames. The first day he made five frames and each day, thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?