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.

Answer 1

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

⇒ 4a – 1200 = 2800

⇒ 4a = 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.