Three vessels P, Q, and R have capacities in the proportion 2 : 3 : 5. Each vessel is filled with a mixture of alcohol and water, where the respective ratios are 1 : 1 in P, 2 : 1 in Q, and 3 : 1 in R. If the entire contents of these three vessels are poured together and mixed thoroughly, what will be the overall ratio of alcohol to water in the combined mixture?
Show answer & explanation
Correct answer: B
Explanation
Given:
Capacities of P : Q : R = 2 : 3 : 5
In P, Alcohol : Water = 1 : 1
In Q, Alcohol : Water = 2 : 1
In R, Alcohol : Water = 3 : 1
Quantity of P = 2
Alcohol = 2 × 1/2 = 1
Water = 2 × 1/2 = 1
Quantity of Q = 3
Alcohol = 3 × 2/3 = 2
Water = 3 × 1/3 = 1
Quantity of R = 5
Alcohol = 5 × 3/4 = 15/4
Water = 5 × 1/4 = 5/4
Total Alcohol = 1 + 2 + 15/4 = 27/4
Total Water = 1 + 1 + 5/4 = 13/4
Alcohol : Water = 27/4 : 13/4 = 27 : 13