Question

A farmer undertakes to pay off a debt of Rs. 2700 by monthly
instalments. He pays Rs. 200 as the first instalment and
increases every subsequent instalment by Rs. 25 over the
immediate previous instalment. In how many instalments his
debt will be cleared up?​

Answer 1

Given :

• A farmer undertakes to pay off a debt of Rs. 2700 by monthly installments.

• He pays Rs. 200 as the first installment and increases every subsequent instalment by Rs. 25 over the immediate previous installment.

To find :

• In how many installments his debt will be cleared up?

Solution :

• Since the farmer increases every subsequent installment by Rs. 25 over the immediate previous installment, we can formulate an Arithmetic Progression whose first term is 200 and common difference is 25.

• Given total debt = Rs. 2700

• Let there be n number of installments

• Then,
• n/2 * [2 * 200 + (n - 1) * 25] = 2700
• or, n/2 * (400 + 25n - 25) = 2700
• or, n/2 * (375 + 25n) = 2700
• or, n (375 + 25n) = 5400
• or, n (15 + n) = 216
• or, n² + 15n - 216 = 0
• or, n² + 24n - 9n - 216 = 0
• or, n (n + 24) - 9 (n + 24) = 0
• or, (n + 24) (n - 9) = 0

• So n = - 24, 9

• Since number of installments cannot be negative, the value of n is 9.

Answer :

• Total number of installments is 9.