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,

S_n = 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