Working efficiencies of A and B for completing a piece of work are in the ratio 7 : 9. The number of days to be taken by them to complete the work will be in the ratio

Options

A. `9:7`
B. `7:9`
C. `4:7`
D. `7:4`

Answer

To solve the problem, we need to determine the ratio of the time taken by A and B to complete the work based on their efficiencies.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The working efficiencies of A and B are given in the ratio of 7:9.
- This means that for every 7 units of work A can do, B can do 9 units of work in the same time.

2. **Define the Efficiency**:
- Let the efficiency of A be 7 units of work per day.
- Let the efficiency of B be 9 units of work per day.

3. **Determine the Total Work**:
- Assume the total work to be done is a common multiple of their efficiencies. For simplicity, we can take the total work as the least common multiple (LCM) of 7 and 9, which is 63 units of work.

4. **Calculate the Time Taken by A**:
- Time taken by A to complete the work = Total Work / Efficiency of A
- Time taken by A = 63 / 7 = 9 days.

5. **Calculate the Time Taken by B**:
- Time taken by B to complete the work = Total Work / Efficiency of B
- Time taken by B = 63 / 9 = 7 days.

6. **Establish the Ratio of Time Taken**:
- The ratio of time taken by A and B = Time taken by A : Time taken by B = 9 : 7.

### Final Answer:
The ratio of the number of days taken by A and B to complete the work is **9 : 7**.

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