A man buys 12 litres of a mixture that contains 20% milk and the rest water.…
2024
A man buys 12 litres of a mixture that contains 20% milk and the rest water. He then mixes it with 10 litres of another mixture that contains 30% milk. What is the percentage of water in the new mixture?
- A.
63.72%
- B.
58.14%
- C.
75.45%
- D.
24.54%
Show answer & explanation
Correct answer: C
Concept
When two mixtures are combined, the amount of any one component (here, water) in the final mixture equals the sum of that component's amount from each part. If a mixture of volume V has water fraction w, the water it contributes is V × w. Adding the water contributed by every part and dividing by the total combined volume gives the water percentage in the final mixture.
Application
First mixture: 12 L with 20% milk, so water = 100% − 20% = 80%. Water volume = 12 × 0.80 = 9.6 L.
Second mixture: 10 L with 30% milk, so water = 100% − 30% = 70%. Water volume = 10 × 0.70 = 7 L.
Total volume of the combined mixture = 12 + 10 = 22 L.
Total water = 9.6 + 7 = 16.6 L.
Percentage of water = (16.6 / 22) × 100 = 75.45%.
Cross-check
Milk volume from each part: 12 × 0.20 = 2.4 L and 10 × 0.30 = 3 L, total milk = 5.4 L. Milk percentage = (5.4 / 22) × 100 ≈ 24.55%, and 100% − 24.55% = 75.45% water — matching the direct calculation.
