A can do a piece of work in 15 days and B is 25% more efficient than A. If A and B both work for 4 days and after 4 days C can complete the remaining work alone in 8 days, then find time taken by A, B and C together to complete the whole work.

Options

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

Answer

To solve the problem step by step, we will follow the logical sequence outlined in the video transcript.

### Step 1: Determine the work done by A
A can complete the work in 15 days. Therefore, the work done by A in one day is:
\[ \text{Work done by A in 1 day} = \frac{1}{15} \text{ of the total work} \]

### Step 2: Determine the efficiency of B
B is 25% more efficient than A. If A's efficiency is represented as 100%, then B's efficiency is:
\[ \text{Efficiency of B} = 100\% + 25\% = 125\% \]
This means B can do the work in fewer days. To find the time taken by B:
\[ \text{Time taken by B} = \frac{100}{125} \times 15 = 12 \text{ days} \]
Thus, the work done by B in one day is:
\[ \text{Work done by B in 1 day} = \frac{1}{12} \text{ of the total work} \]

### Step 3: Calculate the total work
To find the total work, we can use the least common multiple (LCM) of the days taken by A and B:
\[ \text{LCM of 15 and 12} = 60 \text{ units of work} \]

### Step 4: Calculate the daily work of A and B
Now we can calculate the work done by A and B in one day:
- Work done by A in one day = \( \frac{60}{15} = 4 \) units
- Work done by B in one day = \( \frac{60}{12} = 5 \) units

### Step 5: Calculate the work done by A and B in 4 days
In 4 days, A and B together will do:
\[ \text{Total work done by A and B in 4 days} = (4 + 5) \times 4 = 9 \times 4 = 36 \text{ units} \]

### Step 6: Determine the remaining work
The remaining work after A and B have worked for 4 days is:
\[ \text{Remaining work} = 60 - 36 = 24 \text{ units} \]

### Step 7: Determine the efficiency of C
C can complete the remaining work in 8 days, so the work done by C in one day is:
\[ \text{Work done by C in 1 day} = \frac{24}{8} = 3 \text{ units} \]

### Step 8: Calculate the combined efficiency of A, B, and C
Now, we can find the combined efficiency of A, B, and C:
\[ \text{Combined efficiency} = 4 + 5 + 3 = 12 \text{ units per day} \]

### Step 9: Calculate the time taken by A, B, and C together to complete the whole work
To find the time taken by A, B, and C together to complete the entire work of 60 units:
\[ \text{Time taken} = \frac{60}{12} = 5 \text{ days} \]

### Final Answer
The time taken by A, B, and C together to complete the whole work is **5 days**.

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