Sunil and Pradeep can complete a work in 5 days and 15 days respectively. They both work for one day and then Sunil leaves. In how many days will the remaining work completed by Pradeep ?

Options

A. 11 days
B. 12 days
C. 15 days
D. 8 days

Answer

To solve the problem step by step, we will calculate the work done by Sunil and Pradeep, the remaining work after one day, and how long it will take Pradeep to finish the remaining work alone.

### Step 1: Determine the work done by Sunil and Pradeep in one day.
- Sunil can complete the work in 5 days. Therefore, in one day, he completes:
\[ \text{Work done by Sunil in one day} = \frac{1}{5} \text{ of the work} \]

- Pradeep can complete the work in 15 days. Therefore, in one day, he completes:
\[ \text{Work done by Pradeep in one day} = \frac{1}{15} \text{ of the work} \]

### Step 2: Calculate the total work done by both in one day.
- The total work done by both Sunil and Pradeep in one day is:
\[ \text{Total work in one day} = \frac{1}{5} + \frac{1}{15} \]

To add these fractions, we need a common denominator. The least common multiple of 5 and 15 is 15.
- Convert \(\frac{1}{5}\) to have a denominator of 15:
\[ \frac{1}{5} = \frac{3}{15} \]
- Now, add the fractions:
\[ \text{Total work in one day} = \frac{3}{15} + \frac{1}{15} = \frac{4}{15} \]

### Step 3: Calculate the work done after one day.
- After one day of work, the total work completed is \(\frac{4}{15}\). Therefore, the remaining work is:
\[ \text{Remaining work} = 1 - \frac{4}{15} = \frac{15}{15} - \frac{4}{15} = \frac{11}{15} \]

### Step 4: Determine how long it will take Pradeep to complete the remaining work.
- Pradeep completes \(\frac{1}{15}\) of the work in one day. To find out how many days it will take him to complete the remaining \(\frac{11}{15}\) of the work, we use the formula:
\[ \text{Days required} = \frac{\text{Remaining work}}{\text{Work done by Pradeep in one day}} = \frac{\frac{11}{15}}{\frac{1}{15}} = 11 \text{ days} \]

### Conclusion
Pradeep will take 11 days to complete the remaining work after Sunil leaves.

---