Question

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

Answer 1

Correct Answer - ₹ 160, ₹ 140, ₹120, ₹100, ₹ 80, ₹60, ₹40
Let the values of these prizes be ₹x, ₹(x-20), ₹(x-40),… and ₹`(x-20 xx 6)` respectively.
This is an AP with a = x, l = (x-120) and n = 7.
`therefore "sum" = (n)/(2)(a+l) = (7)/(2)(x+x-120) = 7(x-60)`
`rArr 7x - 420 = 700 rArr 7x = 1120 rArr x = 160.`