8 pumps can empty a water tank in 42 hours. How many hours would 56 pumps take to do the same work ?

Options

A. 4
B. 7
C. 5
D. 6

Answer

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

### Step 1: Understand the problem
We know that 8 pumps can empty a water tank in 42 hours. We need to find out how long it would take for 56 pumps to do the same job.

### Step 2: Calculate the total work done by the pumps
The total work done can be represented in terms of pump-hours. If 8 pumps take 42 hours to empty the tank, we can calculate the total work in pump-hours as follows:
\[ \text{Total Work} = \text{Number of Pumps} \times \text{Time} = 8 \text{ pumps} \times 42 \text{ hours} = 336 \text{ pump-hours} \]

### Step 3: Calculate the time taken by 1 pump
Next, we find out how long it would take for a single pump to do the same work:
\[ \text{Time taken by 1 pump} = \frac{\text{Total Work}}{\text{Number of Pumps}} = \frac{336 \text{ pump-hours}}{1 \text{ pump}} = 336 \text{ hours} \]

### Step 4: Calculate the time taken by 56 pumps
Now, we can calculate how long it would take for 56 pumps to empty the water tank:
\[ \text{Time taken by 56 pumps} = \frac{\text{Total Work}}{\text{Number of Pumps}} = \frac{336 \text{ pump-hours}}{56 \text{ pumps}} = 6 \text{ hours} \]

### Final Answer
Thus, 56 pumps would take **6 hours** to empty the water tank.

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