A sum doubles in seven years at simple interest. In how many years will the sum become five times the original sum?

A sum doubles in seven years at simple interest.

P = principal amount

R = rate of interest

T = time

$$2P=P+\frac{\left(P\times\ R\times\ 7\right)}{100}$$

$$2P-P=\frac{\left(P\times\ R\times\ 7\right)}{100}$$

$$P=\frac{\left(P\times\ R\times\ 7\right)}{100}$$

$$R=\frac{100}{7}$$    Eq.(i)

Sum become five times the original sum.

$$5P=P+\frac{\left(P\times\ R\times\ T\right)}{100}$$

$$4P = \frac{\left(P\times\ R\times\ T\right)}{100}$$

$$4=\frac{\ R\times\ T}{100}$$

Put Eq.(i) in the above equation.

$$4=\frac{\ 100\times\ T}{7\times\ 100}$$

$$T=7\times\ 4$$

= 28 years