A man arranges to pay off a debt of Rs. 3600 by 40 annual installments which form an arithmetic series. When 30 of the installments are paid he dies leaving a third of the debt unpaid. Find the value of the first installment.
Text Solution
Verified by Experts51
(51)
Sol. Let first installment be = 'a' and the common difference of the A.P. be ‘d’
So a + (a + d) + (a + 2d) + ....... + (a + 39d) = 3600 ⇒ 
[2a + 39 d] = 3600
⇒ 2a + 39 d = 180 ..... (1)
and 
[2a + 29 d] = 2400
⇒ 2a + 29d = 160 ..... (2)
By equations (1) & (2), we get
d = 2 and a = 51 Ans.
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