Question:
If a bucket is 80% full, then it contains 2 litres more water than when it is \( 66 \frac{2}{3} % \) full. What is the capacity of the bucket?
If a bucket is 80% full, then it contains 2 litres more water than when it is \( 66 \frac{2}{3} % \) full. What is the capacity of the bucket?
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Convert percentages into fractions for easier calculations in capacity-related problems.
Updated On: Mar 7, 2025
- 10 litres
- 15 litres
- \( 16 \frac{2}{3} \) litres
- 20 litres
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The Correct Option is B
Solution and Explanation
Let the total capacity of the bucket be \( x \).
Difference between 80% and \( 66 \frac{2}{3} % \) is: \[ \frac{80}{100}x - \frac{200}{300}x = 2 \] \[ \frac{4}{5}x - \frac{2}{3}x = 2 \] Taking LCM: \[ \frac{12x - 10x}{15} = 2 \] \[ \frac{2x}{15} = 2 \] \[ x = 15 \text{ litres} \] Thus, the correct answer is 15 litres.
Difference between 80% and \( 66 \frac{2}{3} % \) is: \[ \frac{80}{100}x - \frac{200}{300}x = 2 \] \[ \frac{4}{5}x - \frac{2}{3}x = 2 \] Taking LCM: \[ \frac{12x - 10x}{15} = 2 \] \[ \frac{2x}{15} = 2 \] \[ x = 15 \text{ litres} \] Thus, the correct answer is 15 litres.
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