In a chemistry lab two beakers A and B contains 62.5% and 87.5% of spirit…
2017
In a chemistry lab two beakers A and B contains 62.5% and 87.5% of spirit respectively. If two litres from A is mixed with 4 litres of B. The ratio of spirit and water in the resulting mixture is:
- A.
19 : 7
- B.
19 : 6
- C.
19 : 8
- D.
19 : 5
Show answer & explanation
Correct answer: D
Concept
When two solutions of the same substance are combined, the components do not react — they simply add. So the amount of pure spirit in the mixture is the sum of the spirit drawn from each beaker, and the amount of water is the sum of the water drawn from each. The required ratio is then total spirit : total water. For a volume V at concentration c%, spirit = V × c/100 and water = V × (100−c)/100.
Application
From beaker A (62.5% spirit), 2 L is taken. Spirit = 2 × 62.5/100 = 1.25 L, so water = 2 − 1.25 = 0.75 L.
From beaker B (87.5% spirit), 4 L is taken. Spirit = 4 × 87.5/100 = 3.5 L, so water = 4 − 3.5 = 0.5 L.
Total spirit = 1.25 + 3.5 = 4.75 L. Total water = 0.75 + 0.5 = 1.25 L.
Ratio of spirit to water = 4.75 : 1.25. Multiply both terms by 4 to clear decimals: 19 : 5.
So the spirit-to-water ratio in the resulting mixture is 19 : 5.
Cross-check
Total mixture = 2 + 4 = 6 L, and 19 + 5 = 24 parts. Each part = 6/24 = 0.25 L, so spirit = 19 × 0.25 = 4.75 L and water = 5 × 0.25 = 1.25 L — matching the totals above, which confirms the ratio.