Question

A man repays a loan of Rs.32500 by paying Rs.200 in the first month and the increased

payment by Rs. 150 every month. How long will it take him to clear the loan​

Answer 1

Assuming the loan is cleared in ‘n’ months.

Then

The amounts are in A.P with first term(a) as 200 and common difference (d) = 150

Sum of amounts (Sn) = Rs 32500

To calculate number of months we use the formula:-

32500 = n/2 [2 x 200 + (n – 1) 150]

32500 = n/2 [400+150n – 150]

32500 = n/2 [250 + 150n]

65000 = n [250+150n] (Taking 2 on RHS)

65000= 250n+150n2

150n2+250n – 65000 = 0

3n2+5n – 1300 = 0

(n-20) (3n+65) = 0

n = 20 or n = -65/3

Since n cannot be a negative integer,

∴n = 20

Thus, the loan is cleared in 20 months