A tank has a leak which would empty the completely filled tank In 10 hours. If the tank is full of water and a tap is opened which admits 4 litres of water per minute in the tank, the leak takes 15 hours to empty the tank. How many litres of water does the tank hold?

Options

A. 2400
B. 4500
C. 1200
D. 7200

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Define the Variables
Let the capacity of the tank be \( Q \) litres.

### Step 2: Determine the Rate of Leak
The leak can empty the tank in 10 hours. Therefore, the rate of the leak is:
\[ \text{Rate of leak} = \frac{Q}{10} \text{ litres per hour} \]

### Step 3: Determine the Rate of Water Inflow
The tap admits 4 litres of water per minute. To find the rate in litres per hour, we calculate:
\[ \text{Rate of inflow} = 4 \text{ litres/minute} \times 60 \text{ minutes/hour} = 240 \text{ litres/hour} \]

### Step 4: Determine the Effective Rate of Leak with Inflow
When the tap is opened, the tank takes 15 hours to empty. The effective rate of the leak (considering the inflow) can be calculated as:
\[ \text{Effective rate of leak} = \frac{Q}{15} \text{ litres per hour} \]

### Step 5: Set Up the Equation
When the tap is open, the effective rate of water leaving the tank is the rate of the leak minus the rate of inflow:
\[ \frac{Q}{10} - 240 = \frac{Q}{15} \]

### Step 6: Solve the Equation
To solve the equation, we can first eliminate the fractions by finding a common denominator. The common denominator for 10 and 15 is 30. We can multiply the entire equation by 30:
\[ 30 \left(\frac{Q}{10}\right) - 30 \cdot 240 = 30 \left(\frac{Q}{15}\right) \]
This simplifies to:
\[ 3Q - 7200 = 2Q \]

### Step 7: Rearrange the Equation
Now, rearranging gives:
\[ 3Q - 2Q = 7200 \]
\[ Q = 7200 \text{ litres} \]

### Conclusion
Thus, the capacity of the tank is \( 7200 \) litres.

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