A certain sum invested at simple interest amounts to Rs. 10,072 in 3
2
1
​
years and to Rs. 11,552 in 6 years at the same rate per annum. The rate of interest p.a. is:

Let the principal be P and the annual simple interest be I.
Interest for 6−3.5=2.5 years is:

Interest for 2.5 years=11,552−10,072=Rs. 1,480
Interest for 1 year:

I=
2.5
1480
​
=Rs. 592
Interest for 6 years:

Interest for 6 years=592×6=Rs. 3,552
Calculate Principal P:

P=Amount after 6 years−Interest for 6 years
P=11,552−3,552=Rs. 8,000
Calculate Rate of Interest (R):

R=
P
I×100
​
=
8000
592×100
​
=
80
592
​
=7.4%