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Question
A sum of Rs. 700 is to be paid to give seven cash prizes to the students of a school for their overall academic performance. If the cost of each prize is Rs. 20 less than its preceding prize; find the value of each of the prizes.
Solution
Total amount of Prize Sn = Rs. 700
Let the value of the first prize be Rs. a
Number of prizes = n = 7
Let the value of first prize be Rs. a
Depreciation in next prize = Rs. 20
We have,
`S_n = n/2 [2a + (n - 1)d]`
`\implies 700 = 7/2 [2a + 6(-20)]`
`\implies 700 = 7/2 [2a = 120]`
`\implies` 1400 = 14a – 840
`\implies` 14a = 2240
`\implies` a = 160
`\implies` Value of 1st Prize = Rs. 160
Value of 2nd Prize = Rs. (160 – 20) Rs. 140
Value of 3rd Prize = Rs. (140 – 20) = Rs. 120
Value of 4th Prize = Rs. (120 – 20) = Rs. 100
Value of 5th Prize = Rs. (100 – 20) Rs. 80
Value of 6th Prize = Rs. (80 – 20) = Rs. 60
Value of 7th Prize = Rs. (60 – 20) = Rs. 40
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