W and T together can do a work in 12 days. W alone can do the work in 15 days. In how many days can T alone do the work?

Options

A. 65
B. 72
C. 45
D. 60

Answer

To solve the problem, we need to determine how many days T alone can do the work based on the information provided about W and T working together and W working alone.

### Step-by-Step Solution:

1. **Understanding the Work Done Together:**
W and T together can complete the work in 12 days. This means their combined work rate is:
\[ \text{Work rate of W and T together} = \frac{1}{12} \text{ (work per day)} \]

2. **Understanding W's Work Rate:**
W alone can complete the work in 15 days. Therefore, W's work rate is:
\[ \text{Work rate of W} = \frac{1}{15} \text{ (work per day)} \]

3. **Finding T's Work Rate:**
To find T's work rate, we can use the formula for combined work rates:
\[ \text{Work rate of W and T} = \text{Work rate of W} + \text{Work rate of T} \]
Substituting the known values:
\[ \frac{1}{12} = \frac{1}{15} + \text{Work rate of T} \]

4. **Solving for T's Work Rate:**
Rearranging the equation to isolate T's work rate:
\[ \text{Work rate of T} = \frac{1}{12} - \frac{1}{15} \]
To perform this subtraction, we need a common denominator. The least common multiple of 12 and 15 is 60. Thus, we convert both fractions:
\[ \frac{1}{12} = \frac{5}{60} \quad \text{and} \quad \frac{1}{15} = \frac{4}{60} \]
Now substituting these values back into the equation:
\[ \text{Work rate of T} = \frac{5}{60} - \frac{4}{60} = \frac{1}{60} \]

5. **Calculating the Time for T to Complete the Work Alone:**
Since T's work rate is \(\frac{1}{60}\), it means T can complete the entire work in:
\[ \text{Time taken by T} = \frac{1}{\text{Work rate of T}} = \frac{1}{\frac{1}{60}} = 60 \text{ days} \]

### Final Answer:
T alone can do the work in **60 days**.