Three pumps working 8 hours a day can empty a tank in 2 day. How many hours a day must 4 pumps work to empty the tank in 1 day.

Options

A. 10 hours
B. 12 hours
C. 8 hours
D. None of these

Answer

To solve the problem, we need to find out how many hours a day 4 pumps must work to empty the tank in 1 day, given that 3 pumps can empty the tank in 2 days working 8 hours a day.

### Step 1: Calculate the total work done by 3 pumps in 2 days.

The total work done can be calculated as follows:

\[ \text{Total work} = \text{Number of pumps} \times \text{Hours per day} \times \text{Number of days} \]

Substituting the values:

\[ \text{Total work} = 3 \text{ pumps} \times 8 \text{ hours/day} \times 2 \text{ days} = 48 \text{ pump-hours} \]

### Step 2: Determine the work done by 1 pump in 1 hour.

Since the total work is 48 pump-hours, we can find the work done by 1 pump in 1 hour:

\[ \text{Work done by 1 pump in 1 hour} = \frac{48 \text{ pump-hours}}{3 \text{ pumps} \times 16 \text{ hours}} = 1 \text{ tank} \]

### Step 3: Calculate the total work needed to empty the tank in 1 day with 4 pumps.

If we want to empty the tank in 1 day with 4 pumps, the total work required is still the same, which is 48 pump-hours.

### Step 4: Set up the equation for 4 pumps working \( x \) hours a day.

Let \( x \) be the number of hours per day that 4 pumps need to work. The equation for the total work done by 4 pumps in \( x \) hours is:

\[ \text{Total work} = 4 \text{ pumps} \times x \text{ hours} \times 1 \text{ day} = 4x \text{ pump-hours} \]

### Step 5: Equate the total work done to the required work.

We know that the total work needed is 48 pump-hours, so we set up the equation:

\[ 4x = 48 \]

### Step 6: Solve for \( x \).

To find \( x \), we divide both sides of the equation by 4:

\[ x = \frac{48}{4} = 12 \]

### Conclusion:

Thus, 4 pumps must work **12 hours a day** to empty the tank in 1 day.

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