A can do a piece of work in 20 days and B can do same work in 15 days. Both A and B start the work and after some days B left and A complete the remaining work in 6 days. After how many days will B left work?

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Determine the total work
Let’s assume the total work is the least common multiple (LCM) of the days A and B take to complete the work. A can complete the work in 20 days and B in 15 days.

**Calculation:**
- LCM of 20 and 15 = 60 units

### Step 2: Calculate the work done by A and B in one day
Now we can find out how much work A and B can do in one day.

**For A:**
- A's work in one day = Total work / Days taken by A = 60 / 20 = 3 units per day

**For B:**
- B's work in one day = Total work / Days taken by B = 60 / 15 = 4 units per day

### Step 3: Determine the work done by A in 6 days
According to the question, after B leaves, A completes the remaining work in 6 days. We need to find out how much work A does in those 6 days.

**Calculation:**
- Work done by A in 6 days = A's work per day * 6 = 3 * 6 = 18 units

### Step 4: Calculate the remaining work after A's 6 days of work
Now, we can find out how much work is left after A has completed his part in 6 days.

**Calculation:**
- Remaining work = Total work - Work done by A in 6 days = 60 - 18 = 42 units

### Step 5: Set up the equation for the work done by A and B together
Let T be the number of days A and B worked together before B left. The total work done by A and B together is equal to the remaining work.

**Equation:**
- Work done by A and B together = (A's efficiency + B's efficiency) * T
- 42 = (3 + 4) * T
- 42 = 7T

### Step 6: Solve for T
Now we can solve for T.

**Calculation:**
- T = 42 / 7 = 6 days

### Conclusion
B left the work after 6 days.