A and B can do a piece of work in 12 days and 15 days, respectively. They began to work together but B left after 4 days. In how many more days would B alone complete the remaining work?

Options

A. `(20)/(3)`
B. `(25)/(3)`
C. `(24)/(5)`
D. `(20)/(5)`

Answer

To solve the problem step by step, we will calculate the work done by A and B, and then determine how many more days B would take to complete the remaining work after A and B have worked together for 4 days.

### Step 1: Determine the total work
A can complete the work in 12 days, and B can complete it in 15 days. To find the total work, we can take the least common multiple (LCM) of their working days.

- LCM of 12 and 15 is 60.

### Step 2: Calculate the efficiency of A and B
Efficiency is calculated as the total work divided by the time taken to complete that work.

- Efficiency of A = Total Work / Time taken by A = 60 / 12 = 5
- Efficiency of B = Total Work / Time taken by B = 60 / 15 = 4

### Step 3: Calculate the combined efficiency of A and B
When A and B work together, their efficiencies add up.

- Combined efficiency of A and B = Efficiency of A + Efficiency of B = 5 + 4 = 9

### Step 4: Calculate the work done by A and B in 4 days
Now that we know their combined efficiency, we can calculate how much work they complete together in 4 days.

- Work done in 4 days = Combined efficiency × Number of days = 9 × 4 = 36

### Step 5: Calculate the remaining work
Now we can find out how much work is left after A and B have worked together for 4 days.

- Remaining work = Total work - Work done in 4 days = 60 - 36 = 24

### Step 6: Calculate how long it will take for B to complete the remaining work alone
Since B is the one who will complete the remaining work, we need to find out how long it will take B to finish the remaining 24 units of work.

- Time taken by B = Remaining work / Efficiency of B = 24 / 4 = 6 days

### Final Answer
B will take **6 more days** to complete the remaining work alone.

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