A can do a piece of work in 18 days. He worked at it for 12 days and B finished the remaining work in 8 days. B alone can do the whole work in

Options

A. 16 days
B. 24 days
C. 28 days
D. 29 days

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine A's Efficiency
A can complete the work in 18 days. We can assume that the total work is 1800 units (for easier calculations). Thus, A's efficiency can be calculated as:
\[ \text{Efficiency of A} = \frac{\text{Total Work}}{\text{Time taken by A}} = \frac{1800 \text{ units}}{18 \text{ days}} = 100 \text{ units/day} \]

**Hint:** To find efficiency, divide the total work by the time taken to complete that work.

### Step 2: Calculate Work Done by A in 12 Days
A worked for 12 days. The amount of work done by A in these 12 days is:
\[ \text{Work done by A} = \text{Efficiency of A} \times \text{Days worked} = 100 \text{ units/day} \times 12 \text{ days} = 1200 \text{ units} \]

**Hint:** Multiply the efficiency by the number of days worked to find the total work done.

### Step 3: Calculate Remaining Work
The total work is 1800 units, and A has completed 1200 units. Therefore, the remaining work is:
\[ \text{Remaining Work} = \text{Total Work} - \text{Work done by A} = 1800 \text{ units} - 1200 \text{ units} = 600 \text{ units} \]

**Hint:** Subtract the work done from the total work to find out how much is left.

### Step 4: Determine B's Efficiency
B finished the remaining 600 units of work in 8 days. Therefore, B's efficiency can be calculated as:
\[ \text{Efficiency of B} = \frac{\text{Remaining Work}}{\text{Time taken by B}} = \frac{600 \text{ units}}{8 \text{ days}} = 75 \text{ units/day} \]

**Hint:** To find efficiency, divide the amount of work completed by the time taken to complete that work.

### Step 5: Calculate Time for B to Complete the Whole Work Alone
Now, we need to find out how long it would take B to complete the entire 1800 units of work alone. We can use the efficiency of B:
\[ \text{Time taken by B to complete the whole work} = \frac{\text{Total Work}}{\text{Efficiency of B}} = \frac{1800 \text{ units}}{75 \text{ units/day}} = 24 \text{ days} \]

**Hint:** To find the time taken to complete the whole work, divide the total work by the efficiency.

### Conclusion
B alone can complete the whole work in **24 days**.

### Final Answer
B alone can do the whole work in **24 days**.

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