CMAT 2015 Solved Question Paper

Question : 10 of 100

Marks: +1, -0

Mr. Shyam Das is entitled to receive an annual payment from his employer, which for each year is less by

1/10

th of what it was for the previous year. If the first payment is ₹ 10000, then what is the maximum amount he can receive, however long he may live?

Solution:

(d) 1st payment = ₹ 10000
2nd payment = ₹

(10000-1/10×10000)

= ₹ 9000
3rd payment = ₹

(9000-1/10×9000)

= ₹ 8100
Similarly, 4th payment = ₹

(8100-1/10×8100)

= ₹ 7290
5th payment = ₹

(7290-1/10×7290)

= ₹ 6521
We can write, 10000, 9000, 8100, 7290, 6561..... ∞
Which is in GR where a = 10000.
and common ratio, r = 0.9
∴

S_∞

a/{1-r}

\;\;\;\;\;\;\;\;

10000/{1-0.9}

{10000×10}/1

= ₹ 100000

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