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 =
He has to pay 36000 in 40 annual instalments,
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,
From equations (1) & (2)we get,
a = 510 & d = 20
∴The value of the first instalment is Rs.510.