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Answer :
Let the cost of 1st prize be P Rs.
Cost of 2nd prize = P - 20 Rs
And cost of 3rd prize = P - 40 Rs
We can see that the cost of these prizes are in the form of A.P., having common difference as -20 and first term as P.
Thus, a = P and d = -20
Given that, \(S_7 = 700\)
By the formula of sum of nth term, we know,
\(\Rightarrow S_n = {{n} \over {2}} [2a + (n – 1)d]\)
\(\Rightarrow{{7} \over {2}} [2a + (7 – 1)d] = 700\)
\(\Rightarrow{{2a + (6)(-20)} \over {2}} = 100\)
\(\Rightarrow \) a + 3(-20) = 100
\(\Rightarrow \) a - 60 = 100
\(\Rightarrow \) a = 160
Therefore, the value of each of the prizes was Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60, and Rs 40.