The difference between compound and simple interest of 2 years and 3 years on a certain rate of interest p.a. are Rs. 180 and Rs.552 respectively. Find the simple interest in 4 years on the same sum and at the same rate of interest.

Rs .10800

2 year diff. b/w CI and SI = B

3 year diff. b/w CI and SI = 3B + C

ATQ,

B = 180 and

⇒ 3B + C = 552

⇒ 540 + C = 552

⇒ C = 12

* Here, C = x% of B and B = x% of A*

⇒ 12 = x% of 180

⇒ \(\frac{1}{15}\) = x%

Now,

⇒ B = x% of A ⇒ 180 = \(\frac{1}{15}\) × A

⇒ A = 2700 = Simple Interest in 1 year

⇒ Simple Interest in 4 years = 2700 x 4 = 10800

OR

The difference between SI and Ci in three years = 3(Interest on 1st year) + interest on SI earned in 2 years 

552 = 3 x (180) + interest on SI earned in 2 years 

interest on SI earned in 2 years = 552 - 540 = 12

Rate of interest = \(\frac{12}{180}\) x 100 = \(\frac{20}{3}\)%

Simple Interest in 1 year = \(\frac{180x180}{12}\) = 2700

Simple Interest in 4 years = 2700 x 4 = 10800