Problem statement: Find the rate of interest per annum when a certain sum of money at simple interest amounts to Rs. 2520 in 2 years and Rs. 2700 in 5 years.

Solution:

Let the principal be P and the rate of interest be R%.

Calculation for 2 years:
Simple interest for 2 years = Rs. (2520 - P)
Simple interest for 1 year = (2520 - P)/2
Simple interest for 1 year = P*R/100
Therefore, (2520 - P)/2 = P*R/100
Solving this equation, we get P*R = 5040 - 2P

Calculation for 5 years:
Simple interest for 5 years = Rs. (2700 - P)
Simple interest for 1 year = (2700 - P)/5
Simple interest for 1 year = P*R/100
Therefore, (2700 - P)/5 = P*R/100
Solving this equation, we get P*R = 5400 - 5P

Equating P*R:
From the above equations, we get
5040 - 2P = 5400 - 5P
3P = 360
P = 120

Substituting the value of P in any of the above equations, we get
R = 10%

Therefore, the rate of interest per annum is 10%.

Explanation:
The solution is obtained by using the formula for simple interest, which is given by S.I = (P*R*T)/100, where P is the principal, R is the rate of interest, and T is the time period. By equating the simple interest for 2 years and 5 years, we can obtain two equations in P and R. Solving these equations will give us the values of P and R. Finally, we can substitute these values to obtain the rate of interest per annum.