Solution:

Let us assume that Rs. P be the cost of1^st prize

Then the cost of 2^nd prize = Rs. P − 20

And the cost of 3^rd prize = Rs. P − 40

We can see that the prize costs are written as A.P., with a common difference of -20 and a first term of P.

Therefore, a = P and d = −20

Provided that, S₇ = 700

Using the formula of sum of nth term, we know,

S_n = n/2 [2a + (n – 1)d]

7/2 [2a + (7 – 1)d] = 700

a + 3(−20) = 100

a −60 = 100

a = 160

As a result, Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60, and Rs 40 were the value of each prizes.