In what time will the simple interest be 2/5 of the principal at 8% per annum?

Concept

Simple interest is calculated as SI = (P × R × T) / 100, where P is the principal, R is the annual rate of interest, and T is the time in years. When SI is expressed as a fraction of the principal (SI = k × P), the principal P cancels out of the equation, leaving a direct relationship between the fraction k, the rate R, and the time T.

Application

1. Write down the given relationship: SI = 2/5 of P, and R = 8% per annum.

2. Substitute into the simple interest formula: (2/5)P = (P × 8 × T) / 100.

3. Cancel P from both sides: 2/5 = 8T / 100.

4. Cross-multiply: 8T = (2/5) × 100 = 40.

5. Solve for T: T = 40 / 8 = 5 years.

Cross-check

Substituting T = 5 back into SI = (P × R × T)/100 gives SI = (P × 8 × 5)/100 = 40P/100 = (2/5)P, which matches the required ratio exactly.