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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 - Algebra

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Sum

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, Sn = `"n"/2 [2"a" + ("n" - 1)"d"]`

∴ S12 = `12/2 [2"a" + (12 - 1)(- 10)]`

∴ 1140 = 6[2a + 11(– 10)]

∴ 1140 = 6(2a – 110)

∴ `1140/6` = 2a – 110

∴ 190 = 2a – 110

∴ 2a = 300

∴ a = `300/2` = 150

∴ The amount of first instalment is ₹ 150.

Concept: Sum of First n Terms of an AP
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