Question

The simple interest on a certain sum for 8 months at 4% per annum is Rs. 129 less than the simple interest on the same sum for 15 months at 5% per annum. What is the sum?

• A. Rs. 2580
• B. Rs. 2400
• C. Rs. 2529
• D. Rs. 3600

Hint:

Convert months to years by dividing by 12 in simple interest calculations and carefully equate the difference.

Answer 1

The Correct Option is D

Let the principal amount be \(P\).
Simple Interest (SI) formula: \[ SI = \frac{P \times R \times T}{100} \] where \(R\) is rate of interest per annum, and \(T\) is time in years.
Given:
SI for 8 months at 4% per annum = \(\frac{P \times 4 \times \frac{8}{12}}{100} = \frac{8P}{300}\)
SI for 15 months at 5% per annum = \(\frac{P \times 5 \times \frac{15}{12}}{100} = \frac{25P}{400} = \frac{5P}{80}\)
Difference between these interests is Rs. 129:
\[ \frac{5P}{80} - \frac{8P}{300} = 129 \] Multiply both sides by the LCM of 80 and 300, which is 1200:
\[ 1200 \times \left(\frac{5P}{80} - \frac{8P}{300}\right) = 1200 \times 129 \] Calculate each term:
\[ 1200 \times \frac{5P}{80} = 75P \] \[ 1200 \times \frac{8P}{300} = 32P \] So,
\[ 75P - 32P = 1200 \times 129 \] \[ 43P = 154800 \] \[ P = \frac{154800}{43} = 3600 \] Therefore, the sum is Rs. 3600.