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 1^st prize be \(P\).
Cost of 2^nd 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