If 15 pumps of equal capacity can fill a tank in 7 days, then how many extra pumps will be required to fill the tank in 5 days ?

Options

A. 6
B. 7
C. 14
D. 21

Answer

To solve the problem step by step, we will follow a systematic approach:

### Step 1: Understand the given information
We know that 15 pumps can fill a tank in 7 days.

### Step 2: Calculate the total number of pumps needed to fill the tank in 1 day
If 15 pumps can fill the tank in 7 days, we can calculate how many pumps are needed to fill the tank in 1 day.

Using the formula:
\[ \text{Total pumps needed in 1 day} = \text{Pumps} \times \text{Days} \]
\[ \text{Total pumps needed in 1 day} = 15 \text{ pumps} \times 7 \text{ days} = 105 \text{ pumps} \]

### Step 3: Calculate the number of pumps needed to fill the tank in 5 days
Now we need to find out how many pumps (let's call it X) are needed to fill the tank in 5 days.

Using the same logic:
\[ \text{Total pumps needed in 5 days} = X \text{ pumps} \times 5 \text{ days} \]

### Step 4: Set up the equation
Since the total amount of work (in terms of pump-days) is the same, we can set up the equation:
\[ 105 \text{ pumps} = X \text{ pumps} \times 5 \text{ days} \]

### Step 5: Solve for X
Now we can solve for X:
\[ X = \frac{105 \text{ pumps}}{5 \text{ days}} = 21 \text{ pumps} \]

### Step 6: Calculate the extra pumps needed
We initially had 15 pumps. Now we found that we need 21 pumps to fill the tank in 5 days. To find the extra pumps required:
\[ \text{Extra pumps} = X - \text{initial pumps} = 21 - 15 = 6 \text{ extra pumps} \]

### Final Answer
Thus, the number of extra pumps required to fill the tank in 5 days is **6 pumps**.

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