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.

Answer 1

Let the first prize be ‘a’. 

and Second prize is a – 20 and the third prize Is a 40. 

a, (a – 20), (a – 40) ……….. n = 7 

a = a, d = a₂ – a₁ = a – 20 – a 

d = -20 

n = 7, S₇ = ?

2a – 120 = 200 

∴ 2a = 200 + 120 

2a = 320 

∴ a = \(\frac{320}{2}\) = Rs. 160

∴ Each prizes are 

Rs. 160, 140, 120, 100, 80, 60, 40