Simple interest on a certain sum is $\frac{54}{75}$ of the sum. What is the rate of interest per annum if the value of the rate of interest per annum is half the time period (in years) of investment?

6%

Simple interest on a certain sum is \(\frac{54 }{75 }\) of the sum.

So , Let initial sum = 75 & Simple interest = 54

Rate of interest = \(\frac{Time  }{2 }\)

Simple interest = \(\frac{Principal ×Rate × Time }{100}\)

54 = \(\frac{75 × Rate × (2×Rate) }{100}\)

( Rate )² = 36

Rate = 6%