2023 · Q67
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?
Elementary MathematicsRatio and Proportion
- A203 : 117
- B203 : 157
- C172 : 91
- D165 : 88
Explanation
Take capacities 1:2:3 as 60 mL, 120 mL and 180 mL for glasses P, Q and R. Milk fractions are 1/3 in P, 2/5 in Q and 3/4 in R. Milk contributed is 60/3 = 20 from P, 2·120/5 = 48 from Q and 3·180/4 = 135 from R, totalling 203 parts. Water contributed is (60 − 20) + (120 − 48) + (180 − 135) = 40 + 72 + 45 = 157 parts. The final milk-to-water ratio is 203 : 157, option (B).