Algebra
Aptitude

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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

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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.