Ratio of the principal to simple interest is 4:1 . If rate of interest and…

Step-by-Step Solution

To find the number of years, we use the simple interest formula while applying the given ratios and conditions.

1. Understand the given conditions:

   • The ratio of the Principal (P) to Simple Interest (SI) is 4:1. This means P/SI = 4/1, or P = 4 * SI.

   • The rate of interest (R) is equal to the time (T). Let R = T = t.

2. Set up the equation:

   • Use the standard Simple Interest formula: SI = (P * R * T) / 100

   • Substitute P = 4 * SI and R = T = t into the formula:

   • SI = ((4 * SI) * t * t) / 100

3. Solve for t:

   • Divide both sides by SI (assuming SI is non-zero):

   • 1 = (4 * t^2) / 100

   • 1 = t^2 / 25

   • t^2 = 25

   • t = 5

The number of years is 5 years.