A sum of Rs. 2800 is to be used to award four prizes. If each prize after the first is Rs. 200 less than the preceding prize, find the value of each of the prizes.

Question

Philoid · Accepted Answer

Let the first prize be Rs. x. Thus each succeeding prize is Rs. 200 less than the preceding prize.

∴ Second prize is Rs. (x - 200)

Third prize is Rs. (x - 400)

Fourth prize is Rs. (x - 600)

This forms an AP as x, x - 200, x - 400, x - 600.

Since, Total sum of prize amount = 2800.

∴ x + (x - 200) + (x - 400) + (x - 600) = 2800

⇒ 4x - 1200 = 2800

⇒ 4x = 2800 + 1200

⇒ 4x = 4000

⇒ x = 1000

Thus, the first, second, third and fourth prizes are as Rs. 1000, Rs. 800, Rs. 600, Rs. 400.