The simple interest on a certain sum is one-fourth of the sum. If the number of years and the rate of annual interest are numerically equal, then the number of years is

Let the principal be P; the simple interest is one-fourth of the sum, so the interest equals 0.25P. Using the simple interest formula where the rate and time are numerically equal, let the rate and time both be x, giving 0.25P equals P times x times x divided by 100. Canceling P from both sides results in 0.25 equals x squared divided by 100. Multiplying both sides by 100 gives x squared equals 25, so the number of years is 5.

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