Question

From a bucket full of water, \(\frac{3}{10}\)^th of water is taken out. Now, 4 litres of water is added to the bucket. Then, \(\frac{1}{5}\)^th of water is taken out leaving only \(\frac{2}{3}\)^rd of the bucket full. What is the capacity of the bucket?

• A. 25 litres
• B. 30 litres
• C. 27.5 litres
• D. 20 litres

Answer 1

The Correct Option is B

Capacity of the Bucket Calculation 

Step 1: Initial Information

Let the total capacity of the bucket be C liters.
Initially, the bucket is full, so it contains C liters of water.

Step 2: First Water Removal - \( \frac{3}{10} \) of the Water

Amount of water removed:

\[ \frac{3}{10} \times C \]

Amount of water remaining:

\[ C - \frac{3}{10}C = \frac{7}{10}C \]

Step 3: Adding 4 Liters of Water

Total water in the bucket now:

\[ \frac{7}{10}C + 4 \]

Step 4: Second Water Removal - \( \frac{1}{5} \) of the Remaining Water

Amount of water removed:

\[ \frac{1}{5} \times \left( \frac{7}{10}C + 4 \right) \]

Amount of water remaining:

\[ \frac{7}{10}C + 4 - \frac{1}{5} \times \left( \frac{7}{10}C + 4 \right) \]

Step 5: Setting Up the Equation

We are given that the remaining water is \( \frac{2}{3}C \). Therefore:

\[ \frac{7}{10}C + 4 - \frac{1}{5} \times \left( \frac{7}{10}C + 4 \right) = \frac{2}{3}C \]

Step 6: Simplification and Solving for \( C \)

Multiply both sides by 15 to eliminate fractions:

\[ 4 \times \left( \frac{7}{10}C + 4 \right) = 10 \times \frac{2}{3}C \] \[ 4 \times \frac{7}{10}C + 4 \times 4 = \frac{20}{3}C \] \[ C = 30 \]

Step 7: Conclusion

The capacity of the bucket is 30 liters.