Aparna saves Rs. 500 less than Sumit every month. How long will it take Aparna and Sumit to save Rs.6600 and Rs.9600 respectively?

Options

A. 7 months
B. 6 months
C. 4 months
D. 8 months

Answer

To solve the problem, we need to determine how long it will take Aparna and Sumit to save their respective amounts given that Aparna saves Rs. 500 less than Sumit every month.

### Step-by-step Solution:

1. **Define Variables**:
- Let the amount Sumit saves each month be \( S \).
- Therefore, the amount Aparna saves each month will be \( S - 500 \).

2. **Set Up Equations**:
- Sumit wants to save Rs. 9600. The time taken for Sumit to save this amount can be expressed as:
\[ \text{Time for Sumit} = \frac{9600}{S} \]
- Aparna wants to save Rs. 6600. The time taken for Aparna to save this amount can be expressed as:
\[ \text{Time for Aparna} = \frac{6600}{S - 500} \]

3. **Equate the Times**:
- Since we need to find out how long it will take both of them, we can set the two time equations equal to each other:
\[ \frac{9600}{S} = \frac{6600}{S - 500} \]

4. **Cross Multiply**:
- Cross multiplying gives us:
\[ 9600 \cdot (S - 500) = 6600 \cdot S \]

5. **Expand and Rearrange**:
- Expanding the left side:
\[ 9600S - 4800000 = 6600S \]
- Rearranging the equation:
\[ 9600S - 6600S = 4800000 \]
\[ 3000S = 4800000 \]

6. **Solve for S**:
- Dividing both sides by 3000:
\[ S = \frac{4800000}{3000} = 1600 \]

7. **Calculate Time for Each**:
- Now that we have \( S = 1600 \):
- Time for Sumit:
\[ \text{Time for Sumit} = \frac{9600}{1600} = 6 \text{ months} \]
- Time for Aparna:
\[ \text{Time for Aparna} = \frac{6600}{1600 - 500} = \frac{6600}{1100} = 6 \text{ months} \]

### Final Answer:
Both Aparna and Sumit will take **6 months** to save their respective amounts.