The efficiency of work of P and Q are in the ratio 5 : 7. What will be the ratio of number of days taken by them to finish the work?
A. 7:5
B. 3:4
C. 4:3
D. 5:7

Options

A. A
B. D
C. B
D. C

Answer

To solve the problem, we need to find the ratio of the number of days taken by P and Q to finish the work, given that their efficiencies are in the ratio of 5:7.

### Step-by-Step Solution:

1. **Understand the Relationship Between Efficiency and Time**:
- Efficiency and time taken to complete a work are inversely proportional. This means that if one person is more efficient, they will take less time to complete the work.

2. **Set Up the Efficiency Ratios**:
- Let the efficiency of P be 5 units of work per day and the efficiency of Q be 7 units of work per day.

3. **Calculate the Time Taken**:
- If P can do 5 units of work in one day, the number of days P will take to finish the work can be represented as \( \text{Time taken by P} = \frac{1}{\text{Efficiency of P}} = \frac{1}{5} \).
- Similarly, for Q, the number of days taken will be \( \text{Time taken by Q} = \frac{1}{\text{Efficiency of Q}} = \frac{1}{7} \).

4. **Find the Ratio of Time Taken**:
- The ratio of time taken by P to time taken by Q is given by:
\[ \text{Ratio of time taken} = \frac{\text{Time taken by P}}{\text{Time taken by Q}} = \frac{1/5}{1/7} = \frac{7}{5} \]

5. **Express the Ratio**:
- Therefore, the ratio of the number of days taken by P and Q to finish the work is \( 7:5 \).

6. **Select the Correct Option**:
- From the options provided, the correct answer is **A. 7:5**.