3/4 part of a tank is filled with oil. After taking out 60 litres of oil the tank is 2/3 part full. What is the capacity (in litres) of the tank?

Options

A. 240
B. 360
C. 600
D. 720

Answer

To solve the problem, we need to find the total capacity of the tank based on the information given. Let's break it down step by step.

### Step 1: Define the variables
Let the total capacity of the tank be \( C \) litres.

### Step 2: Calculate the initial amount of oil in the tank
According to the problem, \( \frac{3}{4} \) of the tank is filled with oil. Therefore, the amount of oil initially in the tank is:
\[ \text{Initial Oil} = \frac{3}{4}C \]

### Step 3: Determine the amount of oil after removing 60 litres
After taking out 60 litres of oil, the amount of oil left in the tank becomes:
\[ \text{Remaining Oil} = \frac{3}{4}C - 60 \]

### Step 4: Set up the equation based on the new condition
The problem states that after removing 60 litres, the tank is now \( \frac{2}{3} \) full. Therefore, we can express this as:
\[ \text{Remaining Oil} = \frac{2}{3}C \]

### Step 5: Substitute and solve for \( C \)
Now we can set the two expressions for the remaining oil equal to each other:
\[ \frac{3}{4}C - 60 = \frac{2}{3}C \]

### Step 6: Clear the fractions
To eliminate the fractions, we can multiply the entire equation by 12 (the least common multiple of 4 and 3):
\[ 12 \left(\frac{3}{4}C\right) - 12(60) = 12 \left(\frac{2}{3}C\right) \]
This simplifies to:
\[ 9C - 720 = 8C \]

### Step 7: Isolate \( C \)
Now, we can isolate \( C \) by moving \( 8C \) to the left side:
\[ 9C - 8C = 720 \]
\[ C = 720 \]

### Conclusion
The capacity of the tank is \( \boxed{720} \) litres.

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