Question

An amount of money becomes double in 10 years. In how many years will the same amount becomes 5 times of the same rate of simple interest ?

• A. 30
• B. 40
• C. 50
• D. 60

Answer 1

Answer:

B. 40

The same amount of money will become 5 times in 40 years.

1. Find the Rate of Interest

• Let the initial money (Principal) be $P$.

• It becomes double, which means the Amount is $2P$.

• Therefore, the Simple Interest earned is:
  $\text{Interest} = 2P - P = P$

• The time taken is 10 years.

• Using the Simple Interest formula ($\text{Interest} = \frac{P \times R \times T}{100}$):
  $P = \frac{P \times R \times 10}{100}$
  $1 = \frac{R}{10} \implies R = 10\%$

2. Calculate the Time Needed to Become 5 Times

• Now, the money needs to become $5P$.

• The new Simple Interest required is:
  $\text{Interest} = 5P - P = 4P$

• Using the same formula with the 10% interest rate:
  $4P = \frac{P \times 10 \times T}{100}$

• $4 = \frac{T}{10} \implies T = 4 \times 10 = \mathbf{40\text{ years}}$

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Shortcut Method

You can also use this simple formula for such problems:
$\frac{N_1 - 1}{T_1} = \frac{N_2 - 1}{T_2}$

(Where $N$ is the number of times the money multiplies, and $T$ is the time)

$\frac{2 - 1}{10} = \frac{5 - 1}{T_2}$
$\frac{1}{10} = \frac{4}{T_2} \implies T_2 = \mathbf{40\text{ years}}$