10 identical taps fill a tank in 24 minutes. To fill the tank in 1 hour, how many taps are required to be used ?

Options

A. 2
B. 4
C. 6
D. 8

Answer

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

### Step 1: Understand the given information
We know that 10 identical taps can fill a tank in 24 minutes.

### Step 2: Calculate the work done by one tap in one minute
First, we find out how much work is done by 10 taps in one minute.

If 10 taps fill the tank in 24 minutes, then in 1 minute, the fraction of the tank filled by 10 taps is:
\[ \text{Work done by 10 taps in 1 minute} = \frac{1}{24} \text{ of the tank} \]

### Step 3: Calculate the work done by one tap in one minute
Now, to find out how much work is done by one tap in one minute, we divide the work done by 10 taps by 10:
\[ \text{Work done by 1 tap in 1 minute} = \frac{1}{24 \times 10} = \frac{1}{240} \text{ of the tank} \]

### Step 4: Determine the total work needed to fill the tank in 1 hour
We need to fill the tank in 1 hour, which is 60 minutes. Therefore, the total work needed to fill the tank in 1 hour is:
\[ \text{Total work in 1 hour} = 1 \text{ (the whole tank)} \]

### Step 5: Calculate the number of taps required to fill the tank in 1 hour
Let \( x \) be the number of taps required to fill the tank in 1 hour. The work done by \( x \) taps in 1 minute is:
\[ \text{Work done by } x \text{ taps in 1 minute} = x \times \frac{1}{240} \]
In 60 minutes, the work done by \( x \) taps will be:
\[ \text{Total work done by } x \text{ taps in 60 minutes} = 60 \times x \times \frac{1}{240} \]
Setting this equal to 1 (the whole tank):
\[ 60 \times x \times \frac{1}{240} = 1 \]

### Step 6: Solve for \( x \)
Now, we can solve for \( x \):
\[ \frac{60x}{240} = 1 \]
Multiplying both sides by 240:
\[ 60x = 240 \]
Dividing both sides by 60:
\[ x = \frac{240}{60} = 4 \]

### Conclusion
Thus, the number of taps required to fill the tank in 1 hour is **4 taps**.

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