A and B together can do a piece of work in 6 days. If A can
alone do the work in 18 days, hen the number of days
required for B to finish the work is

Options

A. 12
B. 9
C. 15
D. 10

Explanation

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Work Done by A and B
A and B together can complete the work in 6 days. This means that in one day, they can complete \( \frac{1}{6} \) of the work.

### Step 2: Calculate A's Work Rate
A can complete the work alone in 18 days. Therefore, A's work rate is:
\[ \text{Work done by A in one day} = \frac{1}{18} \]

### Step 3: Set Up the Equation for B's Work Rate
Let B take \( x \) days to complete the work alone. Thus, B's work rate is:
\[ \text{Work done by B in one day} = \frac{1}{x} \]

### Step 4: Combine A's and B's Work Rates
Since A and B together complete \( \frac{1}{6} \) of the work in one day, we can set up the equation:
\[ \frac{1}{18} + \frac{1}{x} = \frac{1}{6} \]

### Step 5: Solve the Equation
To solve for \( x \), we first find a common denominator for the fractions. The common denominator of 18, x, and 6 is \( 18x \). Rewriting the equation gives:
\[ \frac{x}{18x} + \frac{18}{18x} = \frac{3x}{18x} \]
This simplifies to:
\[ x + 18 = 3x \]
Now, rearranging gives:
\[ 3x - x = 18 \]
\[ 2x = 18 \]
\[ x = 9 \]

### Step 6: Conclusion
B can complete the work alone in 9 days.