The rates of working of A and B are In the ratio of `2:3`. The number of days taken by each of them to finish the work is in the ratio:

Options

A. `2:3`
B. `4:9`
C. `3:2`
D. `9:4`

Answer

To solve the problem, we need to find the ratio of the number of days taken by A and B to finish the work, given their rates of working.

### Step-by-Step Solution:

1. **Understand the Given Ratio of Efficiency:**
The rates of working of A and B are in the ratio of 2:3. This means:
- Efficiency of A = 2 parts
- Efficiency of B = 3 parts

2. **Define the Work Done:**
Let's assume the total work to be done is a constant amount, say 1 unit of work.

3. **Calculate the Time Taken by Each:**
The time taken to complete the work is inversely proportional to the efficiency. Therefore:
- Time taken by A = Total Work / Efficiency of A = 1 / 2
- Time taken by B = Total Work / Efficiency of B = 1 / 3

4. **Find the Ratio of Days Taken:**
To find the ratio of the days taken by A and B, we take the reciprocal of their efficiencies:
- Ratio of days taken by A to B = (1/2) : (1/3)

5. **Simplify the Ratio:**
To simplify (1/2) : (1/3), we can multiply both sides by 6 (the least common multiple of the denominators):
- (1/2) * 6 : (1/3) * 6 = 3 : 2

6. **Conclusion:**
The ratio of the number of days taken by A and B to finish the work is 3:2.

### Final Answer:
The number of days taken by A and B to finish the work is in the ratio **3:2**.

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