Question

A man pay backs a loan of Rs. 7150 by paying Rs. 120 in the 1st month and then increasing the payment by Rs. 25 every month. How long it takes him to clear the loan.

Answer 1

Solution:-
Assuming that the loan is cleared in 'n' months.
Then, 
The amounts are in AP with first term (a) as 120 and the common difference as 25.
Sum of amounts (Sn) = Rs. 7150
To calculate the number of months we use the following formula.
Sn = n/2{2a + (n -1)d}
7150 = n/2{2 × 120 (n - 1)25}
14300 = n{240 - 25 +25n}
14300 = n{215 + 25n}
25n² + 215n - 14300 = 0
Dividing it by 5, we get.
5n² + 43n - 2860 = 0
5n² - 100n + 143n - 2860 = 0
5n(n - 20) + 143(n - 20) = 0
(n - 20) (5n + 143)
n = 20 or n = -143/5
Since, 'n' cannot be a negative integer, So n = 20 is correct.
Thus, the loan is cleared in 20 months.
Answer.

Answer 2

Sn= n/2 (2a + (n-1)d) 
Sn= 7150 
n= ? 
a= 120 ,2a= 240 
d= 25 
7150= n/2 (240 + (n-1) 25) 
14300= n(215 + 25n) 
14300= 215n + 25n^2 
25n^2 + 215n - 14300 = 0 
5n^2 + 43n -2860 = 0 
5n^2 + 143n - 100n - 2860= 0 
n(5n + 143) - 20( 5n + 143)= 0 
(n - 20)(5n + 143)= 0 
=> n = 20, n = -143/5
n=20