A man arranges to pay off a debt of ₹36000 by 40 annual instalments which form an AP. When 30 of the instalments are paid, he dies, leaving one - third of the debt unpaid. Find the value of the first instalment.
Given: -
Total debt = Rs. 36000
A man pays this debt in 40 annual instalments that forms an A.P.
After annual instalments, that man dies leaving one - third of the debt unpaid.
So,
Within 30 instalments he pays two - thirds of his debt.
Sum of $n$ terms in an Arithmetic Progression $=\frac{n}{2}[2 \times a+(n-1) \times d]$
He has to pay 36000 in 40 annual instalments,
$36000=\frac{40}{2}[2 \times a+(40-1) \times d] \rightarrow(1)$
Where,
$a=$ amount paid in the first instalment,
$d=$ difference between two Consecutive instalments.
He paid two - a third of the debt in 30 instalments,
$\frac{2}{3}(36000)=\frac{30}{2}[2 \times a+(30-1) \times d] \rightarrow(2)$
From equations (1) & (2) we get,
a = 510 & d = 20
∴The value of the first instalment is Rs.510.