If 20 pumps of equal capacity can fill a tank in 7 days, then how many more such pumps will be required to fill the tank in 5 days?

Options

A. 28
B. 16
C. 8
D. 7

Answer

To solve the problem step by step, we will first determine the total work done by the pumps and then calculate how many pumps are needed to fill the tank in the desired time.

### Step 1: Calculate the total work done by the pumps
If 20 pumps can fill the tank in 7 days, we can express the total work done in terms of pump-days.

Total work = Number of pumps × Number of days
Total work = 20 pumps × 7 days = 140 pump-days

### Step 2: Determine the number of pumps required to fill the tank in 5 days
Now, we need to find out how many pumps are required to complete the same amount of work (140 pump-days) in 5 days.

Let \( x \) be the number of pumps required.

Total work = Number of pumps × Number of days
140 pump-days = \( x \) pumps × 5 days

### Step 3: Solve for \( x \)
To find \( x \), we rearrange the equation:

\[ x = \frac{140 \text{ pump-days}}{5 \text{ days}} \]
\[ x = 28 \text{ pumps} \]

### Step 4: Calculate how many more pumps are needed
We already have 20 pumps, so we need to find out how many more pumps are required:

More pumps needed = Total pumps required - Pumps already available
More pumps needed = 28 pumps - 20 pumps = 8 pumps

### Final Answer
Therefore, **8 more pumps** are required to fill the tank in 5 days.

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