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?
- A. 203: 117
- B. 203: 157 ✓
- C. 172: 91
- D. 165: 88
Correct Answer: B. 203: 157
Explanation
Let the capacities be 1, 2, 3 units. Milk fractions are 1/3, 2/5, 3/4. Total milk = 1(\frac{1}{3}) + 2(\frac{2}{5}) + 3(\frac{3}{4}) = \frac{1}{3} + \frac{4}{5} + \frac{9}{4} = \frac{20+48+135}{60} = \frac{203}{60}. Total volume is 1+2+3=6. Total water = 6 - \frac{203}{60} = \frac{360-203}{60} = \frac{157}{60}. Ratio is 203:157.
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