A man repays a loan of Rs. 32500 by paying 200 in the first minth and the increased payment by Rs. 150 every month. How long will it take him to clear the loan?

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.

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