Question

A man arranges to pay off a debt of Rs: 3600 by 40 annual instalments which are in AP. When 30 of the installments are paid, he dies leaving one third of the debt unpaid. The value of the $8^{th}$ instalment is

• A. Rs: 35
• B. Rs: 50
• C. Rs: 65
• D. None of these

Answer 1

The correct option is C Rs: 65

Let the first instalment be $a$ and common difference of AP be $d$.
Given,

$3600=$ sum of 40 term

$\because$ Sum of A.P $S_n=\frac{n}{2}[a+(n-1)d$

$\Rightarrow$$3600=\frac{40}{2}[2a+(40-1\left)d\right]$

Or $3600=20\left[2a+39d\right]or180=2a+39d$ ,...... (i)

After $30$ instalments one-third of the debt is unpaid.

Hence, $\frac{3600}{3}=1200$ is unpaid and $2400$ is paid.

Now, $2400=\frac{30}{2}[2a+(30-1\left)d\right]or160=2a+29d$... ... (ii)
Subtracting Eq. (ii) from Eq. (i),

we get $20=10d$
$\therefore d=2$
From eq. (i),

$180=2a+39\bullet 2$ or $2a=180–78=102$
$\therefore a=51$
Now, value of the $8$ th instalment
$a_8=a+(8-1)d=51+7\times 2=Rs65$