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?

- Rs. 30
- Rs. 40
- Rs. 60
- 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 correctÂ option is B.**