A sum of RS. 700 is used to give seven cash prizes to students of a school for thier overall academic performance. If each prize is Rs. 20 less than it's preceding prize, find the value of each of the prizes.
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160,140,120,100,80,60,40
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Answer:
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, S7 = 700
7/2[2a+(7-1) d] = 700
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.
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