Question

A man arranges to pay off a debt 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 the debt unpaid, find the value of the first instalment.

Answer 1

Let the 40 annual instalments form an arithmetic series of common difference d and first instalment a.

Then, series so formed is

a + (a + d) + (a + 2d) + .... =3600

Or $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

Or $3600=20[2a+39d]$

2a + 39d = 180 ..... (i)

and sum of first 30 terms is $\frac{2}{3}$ of 3600

= 2400

$\Rightarrow 2400=\frac{30}{2}[2a+(29\left)d\right]$

Or 2a + 29d = 160 .... (ii)

From (i) and (ii)

a = 51

The first instalment paid by this man is Rs. 51.