The correct question is:

A farmer borrows Rs.1000 and agrees to repay with a total interest of Rs.140 in 12 installments, each installment preceding by Rs.10

What should be his first installment?

Solution:

Given, total number of installment n = 12

The amount to be paid back = 1000 + 140 = 1140, which is sum of 12 installment.

Let the first installment = x

So, second installment = x - 10

and third installment = 1 - 10 - 10 = x - 20

So, x + (x - 10) + (x - 20) +  .............upto 12 terms = 1140

=> (12/2){2x + (12 - 1)*(-10)} = 1140

=> 6{2x - 110} = 1140

=> 2x - 110 = 1140/6

=> 2x - 110 = 190

=> 2x = 110 + 190

=> 2x = 300

=> x = 300/2

=> x = 150

So, the first installment is Rs. 150