A sum of 2400 amounts to 3,264 in 4 years at a certain rate of simple interest. If the rate of interest is increased by 1%, the same sum in the same time would amount to

Options

A. 3288
B. 3312
C. 3340
D. 3360

Answer

To solve the problem, we need to find out how much the sum of ₹2400 will amount to if the rate of interest is increased by 1% over the same time period of 4 years.

### Step-by-Step Solution:

1. **Identify the given values:**
- Principal (P) = ₹2400
- Amount (A) after 4 years = ₹3264
- Time (T) = 4 years

2. **Calculate the Simple Interest (SI):**
- The formula for Simple Interest is:
\[ SI = A - P \]
- Substitute the values:
\[ SI = 3264 - 2400 = 864 \]

3. **Use the Simple Interest formula to find the rate of interest (R):**
- The formula for Simple Interest is also:
\[ SI = \frac{P \times R \times T}{100} \]
- Rearranging the formula to find R gives:
\[ R = \frac{SI \times 100}{P \times T} \]
- Substitute the known values:
\[ R = \frac{864 \times 100}{2400 \times 4} \]
- Calculate:
\[ R = \frac{86400}{9600} = 9\% \]

4. **Increase the rate of interest by 1%:**
- New Rate (R') = 9% + 1% = 10%

5. **Calculate the new amount (A') using the new rate:**
- Using the Simple Interest formula again:
\[ SI' = \frac{P \times R' \times T}{100} \]
- Substitute the values:
\[ SI' = \frac{2400 \times 10 \times 4}{100} \]
- Calculate:
\[ SI' = \frac{96000}{100} = 960 \]

6. **Find the new amount (A'):**
- The new amount is given by:
\[ A' = P + SI' = 2400 + 960 = 3360 \]

### Final Answer:
The new amount after increasing the rate of interest by 1% over 4 years will be **₹3360**.