In a chemistry lab two beakers A and B contains 36% and 40% of spirit…
2017
In a chemistry lab two beakers A and B contains 36% and 40% of spirit respectively. If two liters from A is mixed with 4 liters of B. The ratio of spirit and water in the resulting mixture is:
- A.
19 : 46
- B.
29 : 46
- C.
29 : 55
- D.
29 : 45
Show answer & explanation
Correct answer: B
Concept
When two liquid solutions are blended, the amount of any component in the mixture is the sum of that component's amount in each part, where component amount = volume × its fractional concentration. The remaining volume is the other component. Once you have the component totals, the required ratio is just one total to the other.
Application
Spirit drawn from A = 2 × 36% = 2 × 0.36 = 0.72 litre.
Spirit drawn from B = 4 × 40% = 4 × 0.40 = 1.60 litre.
Total spirit = 0.72 + 1.60 = 2.32 litre.
Total mixture poured = 2 + 4 = 6 litre.
Water = total − spirit = 6 − 2.32 = 3.68 litre.
Spirit : Water = 2.32 : 3.68. Multiply both by 100 to clear decimals → 232 : 368, then divide by their HCF 8 → 29 : 46.
Cross-check
Scale the answer back: 29 + 46 = 75 parts represent 6 litre, so 1 part = 0.08 litre. Spirit = 29 × 0.08 = 2.32 litre and water = 46 × 0.08 = 3.68 litre, which matches the totals computed above. Hence the ratio of spirit to water is 29 : 46.