Multiple choice

Three glasses P, Q and R have capacities in the ratio 1 : 2 : 3. All these glasses are completely filled with mixtures of milk and water. The ratio of milk to water in P is 1 : 2, in Q it is 2 : 3 and in R it is 3 : 1. If the content of all three glasses are put into a bigger container, what will be the ratio of milk to water in the container?

  1. 203 : 117

  2. 203 : 157

  3. 172 : 91

  4. 165 : 88
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total capacity ratio 1:2:3. Total units = 6. P: 1/3 milk, 2/3 water. Q: 2/5 milk, 3/5 water. R: 3/4 milk, 1/4 water. Total milk = 1*(1/3) + 2*(2/5) + 3*(3/4) = 1/3 + 4/5 + 9/4 = (20+48+135)/60 = 203/60. Total water = 1*(2/3) + 2*(3/5) + 3*(1/4) = 2/3 + 6/5 + 3/4 = (40+72+45)/60 = 157/60. Ratio = 203:157.

AI explanation

Assume the capacities of glasses P, Q and R are 1 liter, 2 liters and 3 liters respectively based on the given ratio. The milk quantities are 1/3 liter in P, 4/5 liter in Q, and 9/4 liters in R, which sum to 203/60 liters. The water quantities are 2/3 liter in P, 6/5 liter in Q, and 3/4 liter in R, summing to 157/60 liters. The final ratio of milk to water is consequently 203:157.

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