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A Farmer Borrows Rs.1,000 and Agrees to Repay with a Total Interest of Rs. 140 in 12 Installments, Each Installment Being Less that the Preceding Installment by Rs. 10. What Should Be His First Installment? - Algebra

A farmer borrows Rs.1,000 and agrees to repay with a total interest of Rs. 140 in 12 installments, each installment being less that the preceding installment by Rs. 10. What should be his first installment?

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Solution

As each installment being less that the preceding installment by Rs. 10 the
installments are in A.P.
S12 = 1000 + 140 = 1140

n = 12, d = -10

`s_n=n/2[2a+(n-1)d]`

`s_12=12/2[2a+(11)(-10)]`

`1140=6[2a-110]`

`1140/6=[2a-110]`

190=[2a-110]

2a=190+110

2a=300

a=300/2

a=150

The first installment = Rs. 150.

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