A farmer borrows Rs. 1000 and agrees to repay with a total interest of Rs. 140 in 12 instalments, each instalment being less than the preceding instalment by Rs. 10. What should be his first instalment?

A farmer borrows Rs. 1000 and agrees to repay with a total interest of Rs. 140 in 12 instalments, each instalment being less than the preceding instalment by Rs. 10. What should be his first instalment?

Sol.

Since a farmer borrows Rs. 1000 and agrees to repay with a total interst of Rs. 140 12 instalments,
we can conclude that,
Sn = 1000 + 140 = Rs. 1140 with n = 12
Since he is paying each instalment being less than the preceding instalment by Rs. 10,
d = - 10.

Now, we need to find the first instalment,
i.e. a  = ?

We Know that,







Sn
=
n
[2a + (n – 1) d





2











1140
=
12
[2a + (12 – 1)(-10)





2











∴ 1140
=
6
[2a – 110)










∴ 1140
=

2a – 110



6













∴ 190
=

2a – 110










∴ 190 + 110
=

2a










∴ 300
=

2a










∴ 300
=

a



2













∴ 150
=

a










∴ a = 150








the amount of first instalment should be Rs. 150