Amount of money = 700
Total number of prize = 7
Each prize is Rs. 20 less than its preceding prize Let,
Prize of first prize = a
Prize of second prize = a – 20
Prize of third prize = a – 20 – 20 = a – 40
Here, A.P. is a, a – 20, a – 40,…
So, common difference, d = a – 20 – a = -20
We Know, Sn = \(\frac{n}{2}\)[2a + (n-1)d]
700 = \(\frac{7}{2}\)[2a + (7-1)-20]
\(\frac{1400}{7}\) =2a + 6(-20)
2a = 200 + 120
2a = 320
a = 160
so, value of first prize = 160
Value of second prize, 160 - 20 = 140
Value of third prize, 140 - 20 = 120
Value of fourth prize 120 - 20 = 100
Value of fifth prize, 100 - 20 = 80
Value of sixth prize, 80 – 20 = 60
And value of seventh prize, 60 – 20 = 40
Hence, value of prizes, Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60, Rs 40.