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

Let the cost of 1st prize be $P$.
Cost of 2nd prize = $P − 20$
And cost of 3rd 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.
$a = P$ and $d = −20$
Given that, $S_7 = 700$
$\frac 72 [2a + (7-1)d] = 700$

$\frac {[2a + (6)(-20)]}{2} = 100$
$a + 3(−20) = 100$
$a − 60 = 100$
$a = 160$
Therefore, the value of each of the prizes was Rs. 160, Rs. 140, Rs. 120, Rs. 100, Rs. 80, Rs. 60, and Rs. 40