A can do a certain job in 15 days. B is 50% more efficient than A. Then B can do the same piece of work in

Options

A. 15
B. 10
C. 12
D. 17

Answer

To solve the problem step by step, we will determine how long it takes for B to complete the same job that A can do in 15 days, given that B is 50% more efficient than A.

### Step-by-Step Solution:

1. **Determine A's Efficiency**:
- A can complete the job in 15 days.
- If we consider A's efficiency as 100 units of work per day, then in 15 days, A completes:
\[ \text{Total Work} = \text{Efficiency of A} \times \text{Time taken by A} = 100 \times 15 = 1500 \text{ units of work} \]

2. **Calculate B's Efficiency**:
- B is 50% more efficient than A.
- Therefore, B's efficiency can be calculated as:
\[ \text{Efficiency of B} = \text{Efficiency of A} + 50\% \text{ of Efficiency of A} = 100 + 50 = 150 \text{ units of work per day} \]

3. **Calculate Time Taken by B**:
- Since both A and B are doing the same amount of work (1500 units), we can set up the equation:
\[ \text{Total Work} = \text{Efficiency of B} \times \text{Time taken by B} \]
- Substituting the known values:
\[ 1500 = 150 \times \text{Time taken by B} \]
- To find the time taken by B, we rearrange the equation:
\[ \text{Time taken by B} = \frac{1500}{150} = 10 \text{ days} \]

4. **Conclusion**:
- Therefore, B can complete the same piece of work in **10 days**.

### Final Answer:
B can do the same piece of work in **10 days**.

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