Three taps A, B and C can fill an tank in 40, 48 and 60 hours respectively. How long (in hours) would the three taps take to fill the tank if all of them are opened together?

Options

A. 12
B. 16
C. 10
D. 8

Answer

To solve the problem of how long it would take for taps A, B, and C to fill a tank together, we can follow these steps:

### Step 1: Determine the rate of each tap
- Tap A can fill the tank in 40 hours. Therefore, in 1 hour, it fills \( \frac{1}{40} \) of the tank.
- Tap B can fill the tank in 48 hours. Therefore, in 1 hour, it fills \( \frac{1}{48} \) of the tank.
- Tap C can fill the tank in 60 hours. Therefore, in 1 hour, it fills \( \frac{1}{60} \) of the tank.

### Step 2: Add the rates of all taps together
To find out how much of the tank is filled when all three taps are opened together in one hour, we add their rates:
\[ \text{Rate of A} + \text{Rate of B} + \text{Rate of C} = \frac{1}{40} + \frac{1}{48} + \frac{1}{60} \]

### Step 3: Find a common denominator
The least common multiple (LCM) of 40, 48, and 60 is 240. We will convert each fraction to have a denominator of 240:
- \( \frac{1}{40} = \frac{6}{240} \) (since \( 240 \div 40 = 6 \))
- \( \frac{1}{48} = \frac{5}{240} \) (since \( 240 \div 48 = 5 \))
- \( \frac{1}{60} = \frac{4}{240} \) (since \( 240 \div 60 = 4 \))

### Step 4: Add the fractions
Now we can add the fractions:
\[ \frac{6}{240} + \frac{5}{240} + \frac{4}{240} = \frac{6 + 5 + 4}{240} = \frac{15}{240} \]

### Step 5: Simplify the result
We can simplify \( \frac{15}{240} \):
\[ \frac{15}{240} = \frac{1}{16} \]
This means that together, taps A, B, and C fill \( \frac{1}{16} \) of the tank in one hour.

### Step 6: Calculate the total time to fill the tank
If they fill \( \frac{1}{16} \) of the tank in one hour, then to fill the entire tank, it would take:
\[ 16 \text{ hours} \]

### Final Answer
Thus, the three taps together would take **16 hours** to fill the tank.

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