`(3)/(4)` part of a tank is full of water. When 30 litres of water is taken out, the tank becomes empty. The capacity of the tank is

Options

A. 36 litres
B. 42 litres
C. 40 litres
D. 38 litres

Answer

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

### Step 1: Understand the problem
The tank is initially filled with water, specifically \( \frac{3}{4} \) of its total capacity. When 30 liters of water is removed, the tank becomes empty.

### Step 2: Define the total capacity of the tank
Let the total capacity of the tank be \( C \) liters.

### Step 3: Calculate the amount of water in the tank
Since \( \frac{3}{4} \) of the tank is full, the amount of water in the tank can be expressed as:
\[ \text{Water in the tank} = \frac{3}{4}C \]

### Step 4: Set up the equation
When 30 liters of water is taken out, the tank becomes empty. This means that the amount of water left in the tank after removing 30 liters is 0. Therefore, we can set up the equation:
\[ \frac{3}{4}C - 30 = 0 \]

### Step 5: Solve for \( C \)
To find the total capacity \( C \), we can rearrange the equation:
\[ \frac{3}{4}C = 30 \]
Now, multiply both sides by \( \frac{4}{3} \) to isolate \( C \):
\[ C = 30 \times \frac{4}{3} \]
Calculating the right side:
\[ C = 30 \times \frac{4}{3} = 40 \]

### Step 6: Conclusion
The total capacity of the tank is \( 40 \) liters.

### Final Answer
The capacity of the tank is **40 liters**.

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