A sum of Rs.700 is to be used to gives even 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 prize.
Amount of money = 700
Total number of prize = 7
Each prize is Rs. 20 less than its preceding prize
Let, Prize of first prize = a
Prize of second prize = a – 20
Prize of third prize = a – 20 – 20 = a – 40
Here, A.P. is a, a – 20, a – 40,…
So, common difference, d = a – 20 – a = -20
We know, Sn = [2a + (n – 1) d]
700 = [2a + (7 – 1) -20]
= 2a + 6 (-20)
2a = 320
a = 160
So, value of first prize = 160
Value of second prize, 160 – 20 = 140
Value of third prize, 140 – 20 = 120
Value of fourth prize, 120 – 20 = 100
Value of fifth prize, 100 – 20 =80
Value of sixth prize, 80 – 20 = 60
And value of seventh prize, 60 – 20 = 40
Hence, value of prizes, Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60, Rs 40.