One of the most important and exam oriented question from arithmetic progression chapter in which we have to find the value of each prize if 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.
Book – RS Aggarwal, Class 10, chapter 5C, question no 45.
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,d=−20
Given that,
S7=700
7/2[2a+(7−1)(−20)]
[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.