P, Q and R together can make a table in 40 minutes. P and Q together can make it in 60 minutes. How much time (in minutes) will R alone take to make the table ?

Options

A. 100
B. 120
C. 90
D. 150

Answer

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

1. **Determine the work done by P, Q, and R together:**
- P, Q, and R can make a table in 40 minutes.
- Therefore, the work done by P, Q, and R together in one minute is:
\[ \text{Work done by P, Q, R in 1 minute} = \frac{1}{40} \]

2. **Determine the work done by P and Q together:**
- P and Q can make the table in 60 minutes.
- Thus, the work done by P and Q together in one minute is:
\[ \text{Work done by P and Q in 1 minute} = \frac{1}{60} \]

3. **Calculate the work done by R alone:**
- The work done by R in one minute can be found by subtracting the work done by P and Q from the work done by P, Q, and R:
\[ \text{Work done by R in 1 minute} = \text{Work done by P, Q, R} - \text{Work done by P and Q} \]
\[ \text{Work done by R in 1 minute} = \frac{1}{40} - \frac{1}{60} \]

4. **Finding a common denominator to perform the subtraction:**
- The least common multiple of 40 and 60 is 120. Thus, we convert the fractions:
\[ \frac{1}{40} = \frac{3}{120} \quad \text{and} \quad \frac{1}{60} = \frac{2}{120} \]
- Now we can perform the subtraction:
\[ \text{Work done by R in 1 minute} = \frac{3}{120} - \frac{2}{120} = \frac{1}{120} \]

5. **Calculate the time R takes to complete the work alone:**
- If R does \(\frac{1}{120}\) of the work in one minute, then R will take:
\[ \text{Time taken by R} = \frac{1}{\frac{1}{120}} = 120 \text{ minutes} \]

Thus, R alone will take **120 minutes** to make the table.