A sum of money at simple interest doubles itself in 4 years 4 months. In how much time will it triple itself?

Correct option is D

Given:

A sum of money doubles itself in 4 years 4 months at Simple Interest (SI).

We need to find the time it takes to triple itself under the same rate.

Formula Used:

Simple Interest (SI) formula:

​$$\text{SI} = \frac{P \times R \times T}{100}$$​​

If a sum doubles, then SI = P

If a sum triples, then SI = 2P

Solution:

Rate (R) when money doubles (SI = P):

​$$P = \frac{P \times R \times \frac{13}{3}}{100} \\ \ \\\Rightarrow R = \frac{100 \times 3}{13} = \frac{300}{13}\%$$​​

Time (T₂) to triple (SI = 2P):

​$$2P = \frac{P \times \frac{300}{13} \times T_2}{100} \\\ \\\Rightarrow 2 = \frac{300}{13 \times 100} \times T_2 \\\ \\\Rightarrow T_2 = \frac{2 \times 1300}{300} = \frac{26}{3} \text{ years} \\ \ \\\Rightarrow T_2 = 8\frac{2}{3}\text{ years}$$​​

Alternate Solution:

If money doubles in $$\frac{13}{3}$$​ years, then:

SI = P is earned in $$\frac{13}{3}$$​years

To earn SI = 2P,

Time required = $$2 \times \frac{13}{3} = \frac{26}{3} \text{ years} = 8\frac{2}{3}\text{ years}$$​​