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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 of the prizes. Q.16

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The best question for class 10th of arithmetic progressions of exercise 5.3 of math . How i solve this question because it is very tough question 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 of the prizes.

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1. Let the cost of 1stÂ prize beÂ Rs. P.

Cost of 2ndÂ prize =Â Rs. PÂ âˆ’ 20

And cost of 3rdÂ prize =Â Rs. PÂ âˆ’ 40

We can see that the cost of these prizes are in the form of A.P., having common difference as âˆ’20 and first term asÂ P.

Thus, aÂ =Â P and dÂ = âˆ’20

Given that,Â S7Â = 700

By the formula of sum of nth term, we know,

SnÂ =Â n/2Â [2aÂ + (nÂ â€“ 1)d]

7/2Â [2aÂ + (7 â€“ 1)d]Â = 700

aÂ + 3(âˆ’20) = 100

aÂ âˆ’60 = 100

aÂ = 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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