A man arranges to pay off a debt of Rs 3600 by 40 annual installments which are in A.P.

A man arranges to pay off a debt of Rs 3600 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. The value of the 8th installment is:

Quiz

Answer/Solution

Rs 65

Steps/Work

Explanation :
Let the first installment be 'a' and the common difference between any two consecutive installments be 'd'
Using the formula for the sum of an A.P :-
S=n/2[2a+(n−1)d].
We have,
3600=40/2[2a+(40-1)d].
3600=20[2a+39d].
180 =2a+39d. ----(i)
Similarly,
2400=30/2[2a+(30-1)d].
160=2a+29d. ----(ii)
On solving both the equations we get:
d=2 and a=51
Hence, the Value of 8th installment is :-
=51+(8−1)2.
=65.
Answer : C