Two taps J and K can fill the tank alone in 60 and 40 hours repectively .If they are opened together ,then in how many hours will the tank be filled ?

Options

A. A)12
B. B)24
C. C)48
D. D)16

Answer

To solve the problem of how long it will take for taps J and K to fill the tank together, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the filling rates of each tap**:
- Tap J can fill the tank in 60 hours. Therefore, its rate of filling is:
\[ \text{Rate of J} = \frac{1}{60} \text{ tank per hour} \]
- Tap K can fill the tank in 40 hours. Therefore, its rate of filling is:
\[ \text{Rate of K} = \frac{1}{40} \text{ tank per hour} \]

2. **Add the rates of both taps**:
- When both taps are opened together, their combined rate of filling the tank is:
\[ \text{Combined Rate} = \text{Rate of J} + \text{Rate of K} = \frac{1}{60} + \frac{1}{40} \]

3. **Find a common denominator to add the fractions**:
- The least common multiple (LCM) of 60 and 40 is 120. We can rewrite the rates with a common denominator:
\[ \frac{1}{60} = \frac{2}{120} \quad \text{and} \quad \frac{1}{40} = \frac{3}{120} \]
- Now, add the two rates:
\[ \text{Combined Rate} = \frac{2}{120} + \frac{3}{120} = \frac{5}{120} = \frac{1}{24} \text{ tank per hour} \]

4. **Calculate the time taken to fill the tank**:
- If the combined rate is \(\frac{1}{24}\) tank per hour, then the time taken to fill one tank is the reciprocal of the combined rate:
\[ \text{Time} = \frac{1}{\text{Combined Rate}} = \frac{1}{\frac{1}{24}} = 24 \text{ hours} \]

### Final Answer:
The tank will be filled in **24 hours** when taps J and K are opened together.