Answer :

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:

S_{n} = [2a + (n - 1)d]

∴ Sum of 7 terms of an AP is given by:

S_{7} = [2a + (7 - 1)d] = 700

⇒ [2*x* + (7 - 1)(-20)] = 700

⇒ 7[2*x* - 120] = 1400

⇒ 2*x* - 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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