A sum lent at simple interest amounts to ₹6,313 in one year and ₹7,139 in 3 years. What is the rate of interest per annum?

Let the Principal amount be P and the annual simple interest earned be I.
According to the problem:

Amount after 1 year:

P+I=6,313
Amount after 3 years:

P+3I=7,139
Subtracting equation (1) from equation (2):

(P+3I)−(P+I)=7,139−6,313
2I=826⟹I=413
So, the simple interest earned per year is ₹413.

Now, substitute I=413 into equation (1) to find the Principal (P):

P+413=6,313⟹P=6,313−413=5,900
The rate of interest per annum (R) can be computed using the formula:

I=
100
P×R×1
​

413=
100
5,900×R
​

413=59R⟹R=
59
413
​
=7%