Ram starts working on a job and works on it for 12 days and completes 40% of the work, To help him complete the work, he employs Ravi and together they work for another 12 days and the work gets completed. How much more efficient is Ram than Ravi?

Options

A. `50%`
B. `200%`
C. `125%`
D. `100%`

Answer

To solve the problem, we need to determine how much work Ram and Ravi can complete individually and then compare their efficiencies.

### Step-by-step Solution:

1. **Determine the total work**:
Let's assume the total work is represented as 100% (or 1 unit of work).

2. **Calculate the work done by Ram**:
Ram works for 12 days and completes 40% of the work. This means:
\[ \text{Work done by Ram in 12 days} = 0.4 \text{ units} \]

3. **Calculate Ram's work rate**:
If Ram completes 0.4 units of work in 12 days, his work rate (R) can be calculated as:
\[ R = \frac{0.4 \text{ units}}{12 \text{ days}} = \frac{1}{30} \text{ units/day} \]

4. **Determine the remaining work**:
After Ram's initial work, the remaining work is:
\[ \text{Remaining work} = 1 - 0.4 = 0.6 \text{ units} \]

5. **Calculate the total work done by Ram and Ravi together**:
Ram and Ravi work together for another 12 days to complete the remaining 0.6 units of work. Let Ravi's work rate be \( r \) units/day. Together, their combined work rate is:
\[ R + r = \frac{1}{30} + r \]
The total work done in 12 days is:
\[ 12 \left( \frac{1}{30} + r \right) = 0.6 \]

6. **Set up the equation**:
Simplifying the equation:
\[ \frac{12}{30} + 12r = 0.6 \]
\[ \frac{2}{5} + 12r = 0.6 \]
Converting 0.6 to a fraction:
\[ 0.6 = \frac{3}{5} \]
Now, substituting:
\[ \frac{2}{5} + 12r = \frac{3}{5} \]

7. **Solve for Ravi's work rate**:
Subtract \(\frac{2}{5}\) from both sides:
\[ 12r = \frac{3}{5} - \frac{2}{5} = \frac{1}{5} \]
Dividing both sides by 12:
\[ r = \frac{1}{5} \times \frac{1}{12} = \frac{1}{60} \text{ units/day} \]

8. **Calculate the efficiency comparison**:
Now we have Ram's work rate \( R = \frac{1}{30} \) units/day and Ravi's work rate \( r = \frac{1}{60} \) units/day.
To find how much more efficient Ram is than Ravi, we compute the ratio of their work rates:
\[ \text{Efficiency Ratio} = \frac{R}{r} = \frac{\frac{1}{30}}{\frac{1}{60}} = \frac{60}{30} = 2 \]

### Conclusion:
Ram is 2 times more efficient than Ravi.