- A sum of money invested for a certain number of years at 8% p.a. simple
interest grows to Rs.180. The same sum of money invested for the same number
of years at 4% p.a. simple interest grows to Rs.120 only. For how many years
was the sum invested?
(1) 25 years (2) 40 years (3) 33 years and 4 months (4) Cannot be determined
Solution:
From the information provided we know that,
Principal + 8% p.a. interest on principal for n years = 180 ��.. (1)
Principal + 4% p.a. interest on principal for n years = 120 ��� (2)
Subtracting equation (2) from equation (1), we get
4% p.a. interest on principal for n years = Rs.60.
Now, we can substitute this value in equation (2),
i.e Principal + 60 = 120
= Principal = Rs.60.
We know that SI = pnr / 100, where p is the principal, n the number of years and r the rate percent of interest.
In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60.
Therefore, 60 = (60*n*4) / 100
=> n = 100/4 = 25 years.
