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A sum of ₹ 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ 20 less than its preceding prize, then what is the value of each prize?

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R s .140, R s .120, R s .100, R s .80, R s .70, R s .60 and R s .40.

R s .150, R s .160, R s .120, R s .110, R s .80, R s .60 and R s . 5 0.

R s .160, R s .140, R s .120, R s .100, R s .80, R s .60 and R s .40.

R s .165, R s .145, R s .125, R s .105, R s .85, R s .65 and R s .45.

answer is C.

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Detailed Solution

Given that the value of each prize is ₹20 less than its preceding prize, so the values of the prizes are in AP with a common difference -20.
Therefore, d = -20.
Let the value of the first prize be Rs.a.
Also, given the total sum of the prizes,

S 7 = 700

.
Formula used for sum of first n term of A.P.:

S n = n 2 [2 a + (n − 1) d]

Applying sum of n terms of an A.P. formula:

∴ S 7 = 72 [2 a + (7 − 1) × (− 20)] ⇒ 700 = 72 × (2 a − 120) ⇒ 700 = 7 a − 420 ⇒ 7 a = 1120 ⇒ a = 160

Therefore, the value of the first prize is Rs.160.
Hence, the value of each prize is

R s .160, R s .140, R s .120, R s .100, R s .80, R s .60 and R s .40.

Hence, option (3) is correct.

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