Q30 of 52 Page 1

A sum of Rs 1,600 is to be used to give ten 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.

Given,


S10 = 1600,


d = - 20


sn = n/2[2a+(n – 1)d]


∴ 10/2[2a+(10 – 1)( - 20)] = 1600


2a – 180 = 320


2a = 320 + 180 = 500


a = 250


1st prize = a = 250


2nd prize = a2 = a+d = 250 + (- 20) = 230


3rd prize = a3 = a2+d = 230 – 20 = 210


4th prize = a4 = a3+d = 210 – 20 = 190


5th prize = a5 = a4+d = 190 – 20 = 170


6th prize = a6 = a5+d = 170 – 20 = 150


7th prize = a7 = a6+d = 150 – 20 = 130


8th prize = a8 = a7+d = 130 – 20 = 110


9th prize = a9 = a8+d = 110 – 20 = 90


10th prize = a10 = a9+d = 210 – 20 = 70


= 16, 00


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