A can do a piece of work in 10 days and B can do it in 15 days. After they have worked together for 4 days, A does away and B completes the remaining work. In how many days B complete the remaining work ?

Options

A. 10
B. 5
C. 15
D. 20

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the work done by A and B in one day.
- A can complete the work in 10 days. Therefore, A's work in one day is:
\[ \text{Work done by A in one day} = \frac{1}{10} \text{ of the work} \]
- B can complete the work in 15 days. Therefore, B's work in one day is:
\[ \text{Work done by B in one day} = \frac{1}{15} \text{ of the work} \]

### Step 2: Find a common unit of work.
- To make calculations easier, we can assume the total work is 30 units (the least common multiple of 10 and 15).
- Thus, A's work in one day:
\[ \text{A's work} = \frac{30}{10} = 3 \text{ units} \]
- B's work in one day:
\[ \text{B's work} = \frac{30}{15} = 2 \text{ units} \]

### Step 3: Calculate the combined work of A and B in one day.
- Together, A and B can do:
\[ \text{Combined work} = 3 + 2 = 5 \text{ units} \]

### Step 4: Calculate the work done by A and B together in 4 days.
- In 4 days, the total work done by A and B is:
\[ \text{Work done in 4 days} = 4 \times 5 = 20 \text{ units} \]

### Step 5: Determine the remaining work.
- The total work is 30 units, and they have completed 20 units together. Therefore, the remaining work is:
\[ \text{Remaining work} = 30 - 20 = 10 \text{ units} \]

### Step 6: Calculate how long it will take B to finish the remaining work.
- B can do 2 units of work in one day. To find out how many days B will take to finish the remaining 10 units, we calculate:
\[ \text{Days taken by B} = \frac{\text{Remaining work}}{\text{B's work in one day}} = \frac{10}{2} = 5 \text{ days} \]

### Conclusion
B will take 5 days to complete the remaining work.

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