4/5 part of a tank is filled with oil. After taking out 42 litres of oil the tank is 3/4 part full. What is the capacity (in litres) of the tank?

Options

A. 420
B. 630
C. 840
D. 1680

Answer

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

### Step 1: Define the capacity of the tank
Let the total capacity of the tank be \( X \) liters.

### Step 2: Determine the initial amount of oil in the tank
According to the problem, \( \frac{4}{5} \) of the tank is filled with oil. Therefore, the amount of oil initially in the tank is:
\[ \text{Initial oil} = \frac{4}{5} X \]

### Step 3: Determine the amount of oil after taking out 42 liters
After removing 42 liters of oil, the tank is \( \frac{3}{4} \) full. Thus, the amount of oil left in the tank is:
\[ \text{Remaining oil} = \frac{3}{4} X \]

### Step 4: Set up the equation
We can set up the equation based on the initial and remaining amounts of oil:
\[ \frac{4}{5} X - 42 = \frac{3}{4} X \]

### Step 5: Solve the equation
To solve for \( X \), first, we will eliminate the fractions by finding a common denominator. The least common multiple of 5 and 4 is 20. We can multiply the entire equation by 20 to eliminate the fractions:
\[ 20 \left( \frac{4}{5} X \right) - 20 \cdot 42 = 20 \left( \frac{3}{4} X \right) \]
This simplifies to:
\[ 16X - 840 = 15X \]

### Step 6: Rearranging the equation
Now, we can rearrange the equation to isolate \( X \):
\[ 16X - 15X = 840 \]
\[ X = 840 \]

### Step 7: Conclusion
The capacity of the tank is \( 840 \) liters.