# Easy Algebra Solved QuestionAptitude Discussion

 Q. A man arranges to pay off a debt of Rs 3600 by 40 annual installments which are in A.P. When 30 of the installments are paid he dies leaving one-third of the debt unpaid. The value of the $8^{th}$ installment is:
 ✖ A. Rs 35 ✖ B. Rs 50 ✔ C. Rs 65 ✖ D. Rs 70

Solution:
Option(C) is correct

Let the first installment be '$a$' and the common difference between any two consecutive installments be '$d$'

Using the formula for the sum of an A.P.
$S=\dfrac{n}{2}[2a+(n−1)d]$
We have,
\begin{align*}
3600&= \dfrac{40}{2}[2a+(40−1)d]\\
\Rightarrow 180&=2a+39d \tag{1} \label{eq1}\\
\text{And }2400&= \dfrac{30}{2}[2a+(30−1)d] \\
\Rightarrow 160&=2a+29d \tag{2} \label{eq2}
\end{align*}
On solving both the equations we get:
$d=2$ and $a=51$

Value of $8^{th}$ installment;

$=51+(8−1)2$
$= \text{Rs. } 65$