Q) A sum of Rs. 1400 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 40 less than the preceding price, find the value of each of the prizes.

Ans: It is given that each prize money is less than the previous prize money by Rs. 40,

So if first student’s prize money is a, next student’s prize money will be (a – 40).

It forms an AP, hence 1st term is a, next term is (a – 40), d = – 40

Since the sum of n terms of an AP,

∴ Sum of 7 terms,

Given that total prize amount is Rs. 1,400

∴

∴

∴ 7(a – 120) = 1400

∴ a – 120 = 200

∴ a = 320

Now, 1st term of this AP will be 320 and next term will be 40 less than previous i.e. 280, and so on for total 7 terms.

Therefore, each of the 7 prizes will be 320, 280, 240, 200, 160, 120 and 80.

Check: Sum of 7 terms = 320 + 280 + 240 + 200 + 160 + 120 + 80 = 1400. This is equal to total prize amount, hence our answer is correct.

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