Question

A sum of Rs.1600 gives a simple interest of Rs. 252 in 2 years and 3 months. The rate of interest per annum is

• A. 5.5%
• B. 8%
• C. 7%
• D. 6%

Hint:

$R = \frac{SI \times 100}{P \times T} = \frac{252 \times 100}{1600 \times 2.25} = \frac{25200}{3600} = 7\%$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Simple interest rate per annum is calculated using standard principal-time-rate relationships.

Step 2: Key Formula or Approach:
Given:
Principal $P = \text{Rs. } 1600$, Simple Interest $SI = \text{Rs. } 252$.
Time $T = 2\,\text{years} + 3\,\text{months} = 2 + \frac{3}{12} = 2.25\,\text{years} = \frac{9}{4}\,\text{years}$.
Formula:
\[SI = \frac{P \times R \times T}{100}\]

Step 3: Detailed Explanation:
Substituting the values:
\[252 = \frac{1600 \times R \times \frac{9}{4}}{100} = 4 \times R \times 9 = 36 R \implies R = \frac{252}{36} = 7\%\]

Step 4: Final Answer:
Hence, the rate of interest per annum is 7%.