A can do work in 18 days. he work at it for 12 days and B finished the remaining work in 8 days. Balon can finish the work in

Options

A. 16 days
B. 24 days
C. 35 days
D. 28 days

Answer

To solve the problem step by step, we need to determine how long Balon can finish the work given the information about A and B.

### Step 1: Determine A's Work Rate
A can complete the work in 18 days. Therefore, A's work rate is:
\[ \text{Work rate of A} = \frac{1}{18} \text{ (work per day)} \]

### Step 2: Calculate Work Done by A in 12 Days
A works for 12 days. The amount of work done by A in this time is:
\[ \text{Work done by A} = 12 \times \frac{1}{18} = \frac{12}{18} = \frac{2}{3} \]

### Step 3: Determine Remaining Work
The total work is considered as 1 (whole work). The remaining work after A has worked for 12 days is:
\[ \text{Remaining work} = 1 - \frac{2}{3} = \frac{1}{3} \]

### Step 4: Determine B's Work Rate
Let’s denote B's work rate as \( \frac{1}{b} \) where \( b \) is the number of days B takes to complete the work alone. We know from the problem that B finishes the remaining work in 8 days. Therefore, the work done by B in 8 days is:
\[ \text{Work done by B} = 8 \times \frac{1}{b} \]
Since B completes the remaining \( \frac{1}{3} \) of the work, we can set up the equation:
\[ 8 \times \frac{1}{b} = \frac{1}{3} \]

### Step 5: Solve for B's Work Rate
Now we can solve for \( b \):
\[ \frac{8}{b} = \frac{1}{3} \]
Cross-multiplying gives:
\[ 8 \cdot 3 = 1 \cdot b \implies b = 24 \]

### Conclusion
Thus, B can finish the work alone in 24 days.

### Summary of Steps:
1. Calculate A's work rate.
2. Find the work done by A in 12 days.
3. Determine the remaining work.
4. Set up the equation for B's work rate based on the remaining work.
5. Solve for B's total time to finish the work.