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

Options

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

Answer

To find the capacity of the tank, let's break down the problem step by step.

### Step 1: Define the capacity of the tank
Let the 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: Calculate the amount of oil after taking out 42 liters
After taking out 42 liters of oil, the tank is now \( \frac{3}{4} \) full. Thus, the amount of oil left in the tank is:
\[ \text{Remaining oil} = \frac{3}{4}x \]

### Step 4: Set up the equation
From the information given, we can set up the following equation:
\[ \frac{4}{5}x - 42 = \frac{3}{4}x \]

### Step 5: Solve the equation
To solve for \( x \), we first 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:
\[ 20 \left(\frac{4}{5}x\right) - 20(42) = 20 \left(\frac{3}{4}x\right) \]
This simplifies to:
\[ 16x - 840 = 15x \]

### Step 6: Rearrange 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.

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