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.

Answer 1

Total amount of Prize S_n = 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 1^st Prize = Rs. 160

Value of 2^nd Prize = Rs. (160 – 20) Rs. 140

Value of 3^rd Prize = Rs. (140 – 20) = Rs. 120

Value of 4^th Prize = Rs. (120 – 20) = Rs. 100 

Value of 5^th Prize = Rs. (100 – 20) Rs. 80

Value of 6^th Prize = Rs. (80 – 20) = Rs. 60

Value of 7^th Prize = Rs. (60 – 20) = Rs. 40