Question

Question 16
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

Let the cost of $1^{st}$ prize be P.
Cost of $2^{nd}$ prize = P − 20
And cost of $3^{rd}$ prize = P − 40
It can be observed that the cost of these prizes are in an A.P. having common difference as −20 and first term as P.
a = P
d = - 20
Given that, $S_7=700$
$\frac{7}{2}[2a+(7-1\left)d\right]=700\frac{7}{2}[2a+(7-1\left)d\right]=700\frac{[2a+(6\left)\right(-20\left)\right]}{2}=100a-3\left(20\right)=100a-60=100a=160$
Therefore, the value of each of the prizes was Rs. 160, Rs. 140, Rs. 120, Rs. 100, Rs. 80, Rs. 60, and Rs. 40.