A can do a piece of work in 10 days, B can do it in 12 days and C can do it in 15 days. In how many days they can complete the work, working together?

Options

A. 6
B. 4
C. 5
D. 10

Answer

To solve the problem step by step, we will follow the outlined process to find out how many days A, B, and C can complete the work together.

### Step 1: Determine the time taken by each worker
- A can complete the work in 10 days.
- B can complete the work in 12 days.
- C can complete the work in 15 days.

### Step 2: Find the total work in terms of a common unit
To find the total work, we can use the Least Common Multiple (LCM) of the days taken by A, B, and C.
- The LCM of 10, 12, and 15 is 60.
So, we can consider the total work to be 60 units.

### Step 3: Calculate the efficiency of each worker
Efficiency is calculated as the total work divided by the time taken.
- Efficiency of A = Total Work / Time taken by A = 60 / 10 = 6 units per day.
- Efficiency of B = Total Work / Time taken by B = 60 / 12 = 5 units per day.
- Efficiency of C = Total Work / Time taken by C = 60 / 15 = 4 units per day.

### Step 4: Calculate the combined efficiency of A, B, and C
Now, we can find the total efficiency when A, B, and C work together:
- Total Efficiency = Efficiency of A + Efficiency of B + Efficiency of C
- Total Efficiency = 6 + 5 + 4 = 15 units per day.

### Step 5: Calculate the time taken to complete the work together
To find the time taken to complete the work together, we can use the formula:
- Time = Total Work / Total Efficiency
- Time = 60 / 15 = 4 days.

### Final Answer
Thus, A, B, and C can complete the work together in **4 days**.

---