Question

₹4000 increased to ₹5000 in 8 years for a certain rate of interest. In years ₹1600 will increase to ₹2400 at the same rate.

• A. 16
• B. 18
• C. 20
• D. 14

Answer 1

The correct option is A 16

Let the rate of interest be $R$.

Given,
Time period, $\left(n\right)=8years$

We know that,
Interest, $I=\frac{PTR}{100}$
$5000-4000=\frac{4000\times 8\times R}{100}R=\frac{1000\times 100}{4000\times 8}R=\frac{25}{8}\%$

In the second case, it is given
$I=₹2400-₹1600=₹800$

Let the time period be $n$ for rate of interest, $\frac{25}{8}\%$.
Then, interest is given by
$800=\frac{1600\times 25\times n}{100\times 8}n=\frac{800\times 8\times 100}{1600\times 25}n=16\text{years}$

$\therefore$ It will take 16 years for ₹1600 to amount to ₹2400 at the same rate.