A sum of Rs.700 has to be used to give seven cash prizes

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

  1. Rs. 30
  2. Rs. 40
  3. Rs. 60
  4. Rs. 80

Answer

Let the least value price be X. Then the next value is X+20, and the next value is X+40 and on and on up to 7 values. So, seven cash prizes follow arithmetic progression with

First term = a (Least prize)

Common difference, d = 20

Number of terms, n = 7

Sum of AP = n/2 [2a + (n-1)d]

Sum = 700 = 7/2 [2*a+(7-1)*20]

700 = 7a + 420

a = 40

The correct option is B.