Glass A contains 100 ml of water and glass B contains 100 ml of wine. A 10 ml spoonful of wine is taken from glass B and mixed thoroughly with the....
water in glass A. A 10 ml spoonful of the mixture from A is returned to B. Is there now more wine in the water or more water in the wine?
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After adding 10 mL of wine to the water, glass A contains 110 mL of liquid at a 10:1 ratio of water to wine, by volume. Since the solution is mixed thoroughly, we can assume that the distribution of wine in the water is constant.
So ten parts of a 10 mL sample is water and one part of it is wine. (10/11)*10mL water + (1/11)*10mL wine = 10 mL.
Glass A now contains (10/11)*100 mL water + (1/11)*100 mL wine.
Glass B now contains (10/11)*10 mL water + (1/11)*10mL wine + 90 mL wine
Glass A now contains 100/11 mL of wine and Glass B contains 100/11 mL of water. They are the same.
Water glass : 100ml water +10 wine . The ratio of water to wine =10:1
Wine glass : 90ml wine.
After second transaction:
water glass: 100(10/11) ml water and 100/11 ml wine. (1)
Wine glass:90+10/11 wine +10*10/11 ml water (2)
Without simplification seeing the status indicated in bold letters at flags (1) and (2) , the answer is obvious that the quantities querried are same./equal.
Wine in water in (1) = 100/11 ml = water in wine (2) = 10*10/11= 100/11 ml
Conclusion: Wine in water glass = water in wine glass = 100/11 ml.
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