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Question
A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment.
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Solution
The installments are in A.P.
Amount repaid in 12 instalments (S12)
= Amount borrowed + Total interest
= 1000 + 140
∴ S12 = 1140
Number of instalments (n) = 12
Each instalment is less than the preceding one by ₹ 10.
∴ d = –10
Now, `S_n = n/2 [2a + (n - 1)d]`
∴ `S_12 = 12/2 [2a + (12 - 1)(-10)]`
∴ 1140 = 6[2a + 11(– 10)]
∴ 1140 = 6(2a – 110)
∴ `1140/6` = 2a – 110
∴ 190 = 2a – 110
∴ 2a = 300
∴ a = `300/2`
∴ a = 150
∴ The amount of first instalment is ₹ 150.
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