If the difference between compound and simple interest on Rs. 25000 at a certain rate R% per annum for 3 years is Rs. 775. If the sum becomes double and rate is increased by 50% then find the difference between compound and simple interest on new sum for 2 years.

Question

Question

Answer 1

Given:

The difference between compound and simple interest for 3 years is Rs. 775

The sum becomes double and rate is increased by 50%

Formula used:

Difference between C.I and S.I for 2 years = P (R/100)²

Difference between C.I and S.I for 3 years = P (R/100)²(3 + R/100)

Calculation:

According to question,

Difference between C.I and S.I for 3 years = Rs. 775

P (R/100)²(3 + R/100) = 775

⇒ 25000 (R²/10000) (3 + R/100) = 775

⇒ R²(300 + R) = 31000

Using "Hit and Trial" Method, if we put R = 10, it equals the RHS, i.e.

So, R = 10%

Now, new principal = 2 × 25000 = Rs. 50000

New rate% = 10 × 150/100 = 15%

So, Difference between C.I and S.I for 2 years = 50000 × (15/100)²

Hence, the required difference = Rs. 1125