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.