# 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.

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.

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