A sum of Rs. 700

Let the first prize be Rs. x. Thus each succeeding prize is Rs. 20 less than the preceding prize.

Second prize, third prize, …, seventh prize be Rs. (x - 20), (x - 40) , …, (x - 120).

This forms an AP as x, x - 20, …, x - 120.

Here, first term = x

Common difference = x - 20 - x = - 20

Total number of terms = 7

Since, Total sum of prize amount = 700.

Sum of all the terms = 700

Now, sum of first n terms of an AP is given by:

Sn = [2a + (n - 1)d]

Sum of 7 terms of an AP is given by:

S7 = [2a + (7 - 1)d] = 700

[2x + (7 - 1)(-20)] = 700

7[2x - 120] = 1400

2x - 120 = 200

x - 60 = 100

x = 160

Thus, the prizes are as Rs. 160, Rs.140, Rs.120, Rs. 100, Rs. 80, Rs. 60, Rs. 40.

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