Working efficiencies of P and Q for completing a piece of work are in the ratio 3:4. The number of days to be taken by them to complete the work will be in the ratio

Options

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

Answer

To solve the problem, we need to find the ratio of the number of days taken by P and Q to complete the work based on their efficiencies.

### Step-by-Step Solution:

1. **Understand the Efficiency Ratio**:
The efficiencies of P and Q are given in the ratio of 3:4. This means if P's efficiency is 3 units of work per day, then Q's efficiency is 4 units of work per day.

2. **Define the Relationship Between Efficiency and Time**:
The time taken to complete work is inversely proportional to efficiency. This means that if efficiency increases, the time taken decreases, and vice versa. The formula for time based on efficiency is:
\[ \text{Time} = \frac{1}{\text{Efficiency}} \]

3. **Calculate the Time Taken by P and Q**:
- For P, the time taken (T_P) can be calculated as:
\[ T_P = \frac{1}{\text{Efficiency of P}} = \frac{1}{3} \]
- For Q, the time taken (T_Q) can be calculated as:
\[ T_Q = \frac{1}{\text{Efficiency of Q}} = \frac{1}{4} \]

4. **Set Up the Ratio of Time Taken**:
Now we need to find the ratio of the time taken by P to the time taken by Q:
\[ \text{Ratio of Time} = T_P : T_Q = \frac{1}{3} : \frac{1}{4} \]

5. **Cross Multiply to Simplify the Ratio**:
To simplify the ratio, we can cross multiply:
\[ \text{Ratio} = \frac{1}{3} : \frac{1}{4} = 4 : 3 \]

6. **Final Result**:
Therefore, the number of days taken by P and Q to complete the work will be in the ratio:
\[ 4 : 3 \]