# Easy Algebra Solved QuestionAptitude Discussion

 Q. A man arranges to pay off a debt of Rs 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 value of the $8^{th}$ instalment is:
 ✖ A. Rs 35 ✖ B. Rs 50 ✔ C. Rs 65 ✖ D. Rs 70

Solution:
Option(C) is correct

Let the first instalment be '$a$' and the common difference between any two consecutive instalments be '$d$'

Using the formula for the sum of an $A.P$.

$S=\dfrac{n}{2}[2a+(n-1)d]$

We have,

$3600=\dfrac{40}{2}[2a+(40-1)d]$

$\Rightarrow 180=2a+39d$-------- (i)

$2400=\dfrac{30}{2}[2a+(30-1)d]$

$\Rightarrow 160=2a+29d$-------- (ii)

On solving both the equations we get:

$d=2$ and $a=51$

Value of $8^{th}$ instalment $=51+(8−1)2$

Rs 65

## (3) Comment(s)

Pawan
()

hey hw to find 8t installment..is der ny formula..how u gt Value of 8th instalment $=51+(8-1)2$

$= \text{Rs. } 65$

Gamer
()

$S_8= a+(8-1)d$

Hence $51 + 7 \times 2 = 65$

Shireesh
()

Yeah Gamer is right.