U, V and W together can make a chair in 20 minutes. U and V together can make it in 25 minutes. How much time will (in minutes) W alone take to make the chair?

Options

A. 100
B. 90
C. 60
D. 120

Answer

To solve the problem step by step, we need to determine how much time W alone will take to make a chair, given the information about U, V, and W working together.

### Step-by-Step Solution:

1. **Understanding the Work Rates**:
- U, V, and W together can make a chair in 20 minutes. This means their combined work rate is:
\[ \text{Work rate of (U + V + W)} = \frac{1 \text{ chair}}{20 \text{ minutes}} = \frac{1}{20} \text{ chairs per minute} \]

2. **Work Rate of U and V**:
- U and V together can make the chair in 25 minutes. Therefore, their combined work rate is:
\[ \text{Work rate of (U + V)} = \frac{1 \text{ chair}}{25 \text{ minutes}} = \frac{1}{25} \text{ chairs per minute} \]

3. **Finding the Work Rate of W**:
- To find W's work rate, we can subtract the work rate of U and V from the work rate of U, V, and W:
\[ \text{Work rate of W} = \text{Work rate of (U + V + W)} - \text{Work rate of (U + V)} \]
\[ \text{Work rate of W} = \frac{1}{20} - \frac{1}{25} \]

4. **Finding a Common Denominator**:
- The least common multiple (LCM) of 20 and 25 is 100. We can rewrite the fractions:
\[ \frac{1}{20} = \frac{5}{100}, \quad \frac{1}{25} = \frac{4}{100} \]
- Now, subtract the two fractions:
\[ \text{Work rate of W} = \frac{5}{100} - \frac{4}{100} = \frac{1}{100} \text{ chairs per minute} \]

5. **Calculating Time for W Alone**:
- If W's work rate is \(\frac{1}{100}\) chairs per minute, then the time taken by W to make 1 chair is the reciprocal of the work rate:
\[ \text{Time taken by W} = \frac{1 \text{ chair}}{\frac{1}{100} \text{ chairs per minute}} = 100 \text{ minutes} \]

### Final Answer:
W alone will take **100 minutes** to make the chair.