A and B can complete a piece of work in 15 days and 10 days, respectively . They work together for 4 days and then B leavs. In how many days will A alone complete the remaining work ?

Options

A. 6
B. 8
C. 5
D. 10

Explanation

To solve the problem step by step, we will first determine the work done by A and B individually, then calculate the work they accomplish together, and finally find out how long A will take to finish the remaining work after B leaves.

### Step 1: Determine the work done by A and B individually.

- A can complete the work in 15 days.
- B can complete the work in 10 days.

To find their work rates (efficiency), we can express the total work in terms of a common unit. Let's assume the total work is 30 units (the least common multiple of 15 and 10).

- Work done by A in one day = Total work / Days taken by A = 30 / 15 = 2 units/day
- Work done by B in one day = Total work / Days taken by B = 30 / 10 = 3 units/day

### Step 2: Calculate the combined work done by A and B in 4 days.

When A and B work together, their combined work rate is:
- Combined work rate = Work done by A + Work done by B = 2 + 3 = 5 units/day

Now, we calculate the work done when they work together for 4 days:
- Work done in 4 days = Combined work rate × Number of days = 5 units/day × 4 days = 20 units

### Step 3: Calculate the remaining work after A and B have worked together.

Total work = 30 units
Work completed by A and B together = 20 units

Remaining work = Total work - Work completed = 30 - 20 = 10 units

### Step 4: Determine how long A will take to complete the remaining work alone.

Now, A will complete the remaining 10 units of work alone. We know A's work rate is 2 units/day.

To find the number of days A will take to complete the remaining work:
- Days taken by A = Remaining work / Work rate of A = 10 units / 2 units/day = 5 days

### Final Answer:
A will take **5 days** to complete the remaining work alone.

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