Question

A man arranges to pay off a dept of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of all debt unpaid, find the value of the first instalment.

Answer 1

In the given problem,

Total amount of debt to be paid in 40 installments

After 30 installments one−third of his debt is left unpaid. This means that he paid two third of the debt in 30 installments. So,

Amount he paid in 30 installments

Let us take the first installment as a and common difference as d.

So, using the formula for the sum of n terms of an A.P,

Let us find a and d, for 30 installments.

Similarly, we find a and d for 40 installments.

Subtracting (1) from (2), we get,

Further solving for d,

Substituting the value of d in (1), we get.

Therefore, the first installment is.