Question

A sum of money doubles itself in two years. Find the time required for it to become 4 times of itself.

• A. 6 years
• B. 4 years
• C. 10 years
• D. 8 years

Answer 1

The correct option is A 6 years

Given, time = 2 years.
Let the sum invested be ₹ 100.
So, the Amount received after two years = ₹ 200.

We know that,
Principal + Interest = Amount.
Hence, Interest = Amount - Principal = ₹ (200-100) = ₹ 100.

The Simple Interest earned on a sum of ₹ P for a period of T years at the rate of R% p.a S.I is given by $\frac{P\times R\times T}{100}$.

So, ₹ 100 = $\frac{100\times R\times 2}{100}$
Hence, R = 50%.

Now, for the amount to become 4 times i.e ₹ 400,
The interest needed to be earned is ₹(400-100) = ₹ 300.
So, ₹ 300 = $\frac{100\times 50\times T}{100}$
Hence, the time taken = T = 6 years.