Three taps A, B and C can fill a tank in 15, 12 and 30 hours respectively. How long (in hours) would the three taps take to fill the tank if all of them are opened together?

Options

A. 60/13
B. 60/11
C. 30/9
D. 7

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 work for each tap
- Tap A can fill the tank in 15 hours, so its rate of work is \( \frac{1}{15} \) of the tank per hour.
- Tap B can fill the tank in 12 hours, so its rate of work is \( \frac{1}{12} \) of the tank per hour.
- Tap C can fill the tank in 30 hours, so its rate of work is \( \frac{1}{30} \) of the tank per hour.

### Step 2: Calculate the combined rate of work
To find the combined rate of work when all three taps are opened together, we add their individual rates:
\[ \text{Combined rate} = \frac{1}{15} + \frac{1}{12} + \frac{1}{30} \]

### Step 3: Find a common denominator
The least common multiple (LCM) of 15, 12, and 30 is 60. We will convert each fraction to have a denominator of 60:
- \( \frac{1}{15} = \frac{4}{60} \)
- \( \frac{1}{12} = \frac{5}{60} \)
- \( \frac{1}{30} = \frac{2}{60} \)

### Step 4: Add the rates
Now we can add the fractions:
\[ \text{Combined rate} = \frac{4}{60} + \frac{5}{60} + \frac{2}{60} = \frac{4 + 5 + 2}{60} = \frac{11}{60} \]

### Step 5: Calculate the time taken to fill the tank
The time taken to fill the tank when all taps are open together can be found by taking the reciprocal of the combined rate:
\[ \text{Time} = \frac{1}{\text{Combined rate}} = \frac{1}{\frac{11}{60}} = \frac{60}{11} \text{ hours} \]

### Final Answer
Thus, the three taps A, B, and C together will take \( \frac{60}{11} \) hours to fill the tank.

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