Question

A man arranges to pay-off a debt of $₹3600$ by $40$ annual instalments, which are in A.P. . When $30$ of the instalments are paid, he dies leaving one-third of the debt unpaid. The $8^{\text{th }}$ instalment is

• A. ₹ 60
• B. ₹ 70
• C. ₹ 65
• D. ₹ 75

Answer 1

Answer: (C)

Here, total debt, $S=₹3600$
and total instalments, $n=40$
Let $a$ and $d$ be the first instalment and increment in instalment.
Thus, we get an A.P. here.
By using sum of $n$ terms, we get
$3600=\frac{40}{2}[2a+(40-1)d]$
$\Rightarrow 180=2a+39d....$(i)
Now, after 30 instalments, one-third of the debt is unpaid.
i.e., $\frac{3600}{3}=₹1200$ is unpaid and then paid money
$=3600-1200=₹2400$
So, again by using sum of $n$ terms, we get
$S_{30}=2400=\frac{30}{2}[2a+(30-1)d]$
$\Rightarrow 160=2a+29d$...(ii)
On solving Eqs. (i) and (ii), we get
$a=51,d=2$
We know that,
$n^{\text{th }}\text{ term }{T}_n=a+(n-1)d$
$\therefore 8^{\text{th }}$ instalment, $T_8=a+(8-1)d$
$=51+7\times 2=51+14=₹65$
Hence, the $8^{\text{th }}$ instalment is $₹65$.