If the ratio of principal and the simple interest for 5 years is 10 : 7, then the rate of interest (per annum)is:

If the ratio of principal and the simple interest for 5 years is 10 : 7.

Let's assume the principal and the simple interest for 5 years is 10y and 7y respectively.

$$simple\ interest=\frac{P\times\ R\times\ T}{100}$$

Where P = principal amount, R = rate of interest, T = time.

$$7y=\frac{10y\times\ R\times\ 5}{100}$$

$$7=\frac{10\times\ R\times\ 5}{100}$$

$$7=\frac{50\ R}{100}$$

$$7=\frac{R}{2}$$

$$R=7\times\ 2$$

Rate of interest = R = 14%