Question

A certain sum becomes 8 fold in 15 years at simple interest. What will be the rate of interest?

• A. 46 \(\frac{1}{3}\)%
• B. 46 \(\frac{2}{3}\)%
• C. 46 \(\frac{3}{4}\)%
• D. 46 \(\frac{3}{5}\)%

Hint:

For simple interest, use the relation SI = Amount - Principal and substitute values to find the rate.

Answer 1

The Correct Option is B

Step 1: Given
Final amount = 8 times the principal
Time = 15 years
Step 2: Simple interest formula
\[ A = P + SI \] Where,
\(SI = \frac{P \times R \times T}{100}\), \(A\) is amount, \(P\) is principal, \(R\) is rate, \(T\) is time.
Step 3: Calculate SI
Since \(A = 8P\),
\[ SI = A - P = 8P - P = 7P \] Step 4: Substitute into SI formula
\[ 7P = \frac{P \times R \times 15}{100} \] \[ 7 = \frac{15R}{100} \] \[ R = \frac{7 \times 100}{15} = \frac{700}{15} = 46.\overline{6}% \] This is 46 \(\frac{2}{3}\)%
Thus, Option (B) is correct.