If Rs 420 is divided between A and B in the ratio `3 : 4` then A's share is ?

Options

A. Rs 180
B. Rs 240
C. Rs 270
D. Rs 210

Answer

To find A's share when Rs 420 is divided between A and B in the ratio of 3:4, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Ratio**: The ratio given is 3:4. This means for every 3 parts A receives, B receives 4 parts.

2. **Calculate the Total Parts**:
\[ \text{Total parts} = 3 + 4 = 7 \]

3. **Determine A's Share**:
A's share is represented by the 3 parts of the total 7 parts. To find A's share, we can use the formula:
\[ \text{A's share} = \left(\frac{\text{A's ratio}}{\text{Total ratio}}\right) \times \text{Total amount} \]
Substituting the values we have:
\[ \text{A's share} = \left(\frac{3}{7}\right) \times 420 \]

4. **Calculate A's Share**:
\[ \text{A's share} = \frac{3 \times 420}{7} \]
First, calculate \( 3 \times 420 = 1260 \).
Now divide \( 1260 \) by \( 7 \):
\[ \text{A's share} = \frac{1260}{7} = 180 \]

5. **Conclusion**:
A's share is Rs 180.

### Summary:
A's share when Rs 420 is divided between A and B in the ratio of 3:4 is Rs 180.