Raja and Baja working alone can do a work in 20 days and 15 days respectively. They stared the work together but Baja left after sometime and Raja finished remaining work in 6 days. Find after how many days from start Baja left the work?

Options

A. 5 days
B. 4 days
C. 6 days
D. 3 days

Explanation

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

### Step 1: Determine the efficiencies of Raja and Baja
- Raja can complete the work in 20 days, so his efficiency is:
\[ \text{Efficiency of Raja} = \frac{1}{20} \text{ work/day} = 3 \text{ units/day} \]
- Baja can complete the work in 15 days, so his efficiency is:
\[ \text{Efficiency of Baja} = \frac{1}{15} \text{ work/day} = 4 \text{ units/day} \]

### Step 2: Calculate the total work
- The least common multiple (LCM) of 20 and 15 is 60, which we will take as the total work:
\[ \text{Total Work} = 60 \text{ units} \]

### Step 3: Calculate the work done by Raja in the last 6 days
- Raja finishes the remaining work in 6 days. The work done by Raja in these 6 days is:
\[ \text{Work done by Raja} = \text{Days} \times \text{Efficiency} = 6 \times 3 = 18 \text{ units} \]

### Step 4: Calculate the remaining work after Raja's contribution
- The remaining work after Raja's contribution is:
\[ \text{Remaining Work} = \text{Total Work} - \text{Work done by Raja} = 60 - 18 = 42 \text{ units} \]

### Step 5: Calculate the time taken by Raja and Baja to complete the 42 units of work together
- The combined efficiency of Raja and Baja working together is:
\[ \text{Combined Efficiency} = \text{Efficiency of Raja} + \text{Efficiency of Baja} = 3 + 4 = 7 \text{ units/day} \]
- The time taken to complete the 42 units of work is:
\[ \text{Time} = \frac{\text{Remaining Work}}{\text{Combined Efficiency}} = \frac{42}{7} = 6 \text{ days} \]

### Step 6: Conclusion
- Since they worked together for 6 days before Baja left, the answer is:
\[ \text{Baja left after } 6 \text{ days.} \]