Hemant and Vikash working together can make a wall in 15 days. They both started building the wall and after 3 days Hemant left and Vikash alone build the remaining wall in 24 more days. Find efficiency of Hemant is what percent of Vikash's.

Options

A. 0.5
B. 0.2
C. 0.25
D. 1

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the total work done by Hemant and Vikash together.
Hemant and Vikash can complete the wall together in 15 days. Therefore, the total work can be represented as:
\[ \text{Total Work} = 1 \text{ wall} \]

Since they complete the wall in 15 days, their combined efficiency (work done per day) is:
\[ \text{Combined Efficiency} = \frac{1 \text{ wall}}{15 \text{ days}} = \frac{1}{15} \text{ walls per day} \]

### Step 2: Calculate the work done in the first 3 days.
In the first 3 days, Hemant and Vikash work together. The work done in these 3 days is:
\[ \text{Work done in 3 days} = 3 \times \text{Combined Efficiency} = 3 \times \frac{1}{15} = \frac{3}{15} = \frac{1}{5} \text{ walls} \]

### Step 3: Calculate the remaining work.
After 3 days, the remaining work is:
\[ \text{Remaining Work} = 1 - \frac{1}{5} = \frac{4}{5} \text{ walls} \]

### Step 4: Calculate Vikash's efficiency.
Vikash completes the remaining \(\frac{4}{5}\) wall in 24 days. Therefore, Vikash's efficiency is:
\[ \text{Vikash's Efficiency} = \frac{\text{Remaining Work}}{\text{Time taken}} = \frac{\frac{4}{5} \text{ walls}}{24 \text{ days}} = \frac{4}{5 \times 24} = \frac{4}{120} = \frac{1}{30} \text{ walls per day} \]

### Step 5: Calculate Hemant's efficiency.
Let Hemant's efficiency be \(h\). Since together their efficiency is \(\frac{1}{15}\):
\[ h + \frac{1}{30} = \frac{1}{15} \]

To find \(h\), we can rearrange the equation:
\[ h = \frac{1}{15} - \frac{1}{30} \]

Finding a common denominator (which is 30):
\[ h = \frac{2}{30} - \frac{1}{30} = \frac{1}{30} \text{ walls per day} \]

### Step 6: Calculate the percentage of Hemant's efficiency compared to Vikash's.
Now we need to find what percent Hemant's efficiency is of Vikash's efficiency:
\[ \text{Percentage} = \left( \frac{h}{\text{Vikash's Efficiency}} \right) \times 100 \]
\[ = \left( \frac{\frac{1}{30}}{\frac{1}{30}} \right) \times 100 = 1 \times 100 = 100\% \]

### Conclusion:
Hemant's efficiency is 100% of Vikash's efficiency.