Three different mixtures contain glucose and alcohol with glucose concentrations of 12%, 35%, and 45% respectively. If 2 litres from the first vessel, 3 litres from the second vessel, and 1 litre from the third vessel are mixed together, what will be.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:This problem tests mixture composition using weighted averages. When you combine liquids from multiple sources with different percentages, the correct way is to compute the absolute amount of the ingredient (glucose) contributed by each portion, sum them, and then compare with the remaining part (alcohol). The final ratio is based on total glucose and total alcohol in the combined volume. Given Data / Assumptions: Vessel 1 glucose = 12% Vessel 2 glucose = 35% Vessel 3 glucose = 45% Volumes mixed: 2 L, 3 L, 1 L respectively Each mixture contains only glucose and alcohol Concept / Approach:Glucose amount = (percentage/100) * volume. Alcohol amount = total volume - total glucose. Then form the ratio glucose:alcohol and simplify. Step-by-Step Solution: Step 1: Glucose from vessel 1 = 0.12 * 2 = 0.24 L Step 2: Glucose from vessel 2 = 0.35 * 3 = 1.05 L Step 3: Glucose from vessel 3 = 0.45 * 1 = 0.45 L Step 4: Total glucose = 0.24 + 1.05 + 0.45 = 1.74 L Step 5: Total volume mixed = 2 + 3 + 1 = 6 L Step 6: Total alcohol = 6 - 1.74 = 4.26 L Step 7: Ratio glucose:alcohol = 1.74 : 4.26 Step 8: Multiply both by 100 to avoid decimals: 174 : 426 Step 9: Simplify by dividing by 6: 174/6 = 29 and 426/6 = 71 Step 10: Final ratio = 29:71 Verification / Alternative check:Glucose fraction in final mix = 1.74/6 = 0.29 = 29%. Alcohol fraction = 71%. Ratio 29:71 is consistent with the computed percentage split. Why Other Options Are Wrong: 71:29: reverses glucose and alcohol. 87:213: equals 29:71 but not simplified; question asks ratio form typically simplified. 31:69: would imply glucose 31%, which is higher than computed. 35:65: would incorrectly assume the result equals one vessel percentage. Common Pitfalls:A common mistake is to average the percentages directly: (12 + 35 + 45)/3, which ignores unequal volumes. Always weight by volume. Another mistake is to forget to compute alcohol as the remainder after total glucose is found. Final Answer:29:71

More Questions from Alligation or Mixture

Discussion & Comments