A sum of money lent at simple interest amounts to Rs. 7,920 in 2 years and to Rs. 11,220 after 5 more years. What is the rate of interest per annum?

Let the principal be P and the annual simple interest be I.
Amount after 2 years = P+2I=7920

Amount after 5 more years (2+5=7 years) = P+7I=11220

Subtract the first equation from the second:

(P+7I)−(P+2I)=11220−7920
5I=3300
I=
5
3300
​
=Rs. 660 per year
Now find the principal (P):

P+2(660)=7920
P+1320=7920
P=7920−1320=Rs. 6600
Now find the rate of interest (R):

I=
100
P×R×1
​

660=
100
6600×R×1
​

660=66×R⟹R=
66
660
​
=10%