Question

A man arranges to pay off a debt of Rs. $36000$ 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. Find the first installment.

• A. Rs. $1200$
• B. Rs. $1025$
• C. Rs. $1024$
• D. Rs. $560$

Answer 1

Answer: (D)

Rs. $560$

Given:

n=40

$S=36000=\frac{40}{2}[2a+(40-1\left)d\right]$

$\Rightarrow 2a+39d=1800$ .....eq( 1 )

Now,

$S^{{}^{\prime }}=\frac{2}{3}.36000=24000$ when n = 30

$\Rightarrow 24000=\frac{30}{2}[2a+(30-1\left)d\right]$

$\Rightarrow 2a+29d=1600$ .....eq( 2 )

From eq(1) and eq(2),

$\Rightarrow 10d=200$ [eq( 1 ) - eq( 2 )]

$\therefore d=20$

$\therefore a=560$

$\therefore$ First installment = Rs. 560