A sum of rupay 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is rupay 20 less than its preceding prize, find the value of each of the prizes.

Let the amount for first prize = Rs x
number of prizes = 7
Total prize amount = Rs 700
Therefore, the series of 7 prizes are as follows:
(x) + (x – 20) + (x – 40) + (x – 60) + (x – 80) + (x – 100) + (x – 120) = 700
⇒ 7x – 420 = 700
⇒ 7x = 1120
⇒ x = 1120/7 = 160
Hence, the seven prizes are Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60 and Rs 40.