**Question:**

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

**Solution:**

Let the amount of the first prize be ₹*a*.

Since each prize after the first is ₹200 less than the preceding prize, so the amounts of the four prizes are in AP.

Amount of the second prize = ₹(*a *− 200)

Amount of the third prize = ₹(*a *− 2 × 200) = ₹(*a *− 400)

Amount of the fourth prize = ₹(*a *− 3 × 200) = ₹(*a *− 600)

Now,

Total sum of the four prizes = ₹2,800

∴ ₹*a *+ ₹(*a *− 200) + ₹(*a *− 400) + ₹(*a *− 600) = ₹2,800

⇒ 4*a *− 1200 = 2800

⇒ 4*a *= 2800 + 1200 = 4000

⇒ *a* = 1000

∴ Amount of the first prize = ₹1,000

Amount of the second prize = ₹(1000 − 200) = ₹800

Amount of the third prize = ₹(1000 − 400) = ₹600

Amount of the fourth prize = ₹(* *1000 − 600) = ₹400

Hence, the value of each of the prizes is ₹1,000, ₹800, ₹600 and ₹400.