Ajit is 3 times as efficient as Bablu, then the ratio of number of days required by each to work alone, completely?

Options

A. `3:1`
B. `1:3`
C. `6:3`
D. `3:6`

Answer

To solve the problem, we need to find the ratio of the number of days required by Ajit and Bablu to complete a work alone, given that Ajit is 3 times as efficient as Bablu.

### Step-by-Step Solution:

1. **Define the Efficiency**:
- Let the efficiency of Bablu be \( E_B = 1 \) unit of work per day.
- Since Ajit is 3 times as efficient as Bablu, his efficiency will be \( E_A = 3 \) units of work per day.

2. **Understanding the Relationship**:
- Efficiency is defined as the amount of work done per unit time. Therefore, if the efficiency increases, the time taken to complete the work decreases.
- The formula relating efficiency and time is:
\[ \text{Efficiency} = \frac{\text{Work}}{\text{Time}} \]
- If we consider the total work to be constant, the efficiency and time are inversely proportional.

3. **Setting Up the Ratio of Efficiencies**:
- The ratio of the efficiencies of Ajit and Bablu can be expressed as:
\[ \frac{E_A}{E_B} = \frac{3}{1} \]

4. **Finding the Ratio of Time Taken**:
- Since time is inversely proportional to efficiency, the ratio of the time taken by Ajit (T_A) to the time taken by Bablu (T_B) will be the inverse of their efficiency ratio:
\[ \frac{T_A}{T_B} = \frac{1}{3} \]

5. **Expressing the Ratio**:
- Therefore, the ratio of the number of days required by Ajit to Bablu is:
\[ T_A : T_B = 1 : 3 \]

### Final Answer:
The ratio of the number of days required by Ajit and Bablu to work alone is \( 1 : 3 \).

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