The ratio of spirit and water in solution A is 6 : 7 and the ratio of water…
2023
The ratio of spirit and water in solution A is 6 : 7 and the ratio of water and spirit in solution B is 9 : 4. 3 L of A is mixed with 5 L of B. In 780 mL of the resulting solution, what is the quantity (in mL) of spirit?
Answer: A. 285 — Key idea: find the amount of spirit contributed by each solution, get the spirit fraction of the final mixture, then apply it to 780 mL. Solution A:…
- A.
285
- B.
304
- C.
270
- D.
266
Attempted by 64 students.
Show answer & explanation
Correct answer: A
Key idea: find the amount of spirit contributed by each solution, get the spirit fraction of the final mixture, then apply it to 780 mL.
Solution A: spirit:water = 6:7 → spirit fraction = 6/(6+7) = 6/13. Spirit in 3 L = 3 × 6/13 = 18/13 L.
Solution B: water:spirit = 9:4 → spirit fraction = 4/(9+4) = 4/13. Spirit in 5 L = 5 × 4/13 = 20/13 L.
Total spirit in the mixture = 18/13 + 20/13 = 38/13 L.
Total mixture volume = 3 + 5 = 8 L. Spirit fraction in the final mixture = (38/13) / 8 = 38/104 = 19/52.
In 780 mL of the final mixture: spirit = 780 × 19/52 = (780/52) × 19 = 15 × 19 = 285 mL.
Answer: 285 mL