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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, find the value of each prize.

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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.

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1 Answer

  1. Let the cost of 1st prize be P.
    Cost of 2nd prize =P20
    And cost of 3rd prize P40
    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+(71)(20)]

    [2a+6(−20)​]/2=100
    a+3(20)=100
    a60=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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