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Answer to Q119
One bottle contains 100 liters of wine, another 100 liters of water. Ten liters of wine is moved from the wine bottle to the water bottle and properly mixed in. Ten liters of the mixture is then moved from the water bottle to the wine bottle.
Which of the below statement is correct?
Wine bottle = 100 liters
Water bottle = 100 liters
Ten liters of wine is moved from the wine bottle to the water bottle and properly mixed in.
Now,
Wine bottle is 90 liters
Water bottle is 110 liters
But water bottle contains 100 liters of water and 10 liters of wine. That is ratio 100:10 which is same as 10:1
Ten liters of the mixture is then moved from the water bottle to the wine bottle.
10 liters of the mixture at ratio 10:1 will contain the following
Water = (10 ÷ 11) x 10 liters = 9.09 liters
Wine = (1 ÷ 11) x 10 liters = 0.91 liters
What's now in the wine bottle?
Wine bottle previously had 90 liters of wine.
Then mixture of 0.91 liters of wine and 9.09 liters water was added to it
So it now has 90 + 0.91 = 90.91 liters of wine
What's now in the water bottle?
Water bottle previously had 110 liters of mixture which was 100 liters of water and 10 liters of wine.
Then mixture of 0.91 liters of wine and 9.09 liters water was removed from it.
So it now has 100 - 9.09 = 90.91 liters of water
So, we have 90.91 liters of wine in the wine bottle and 90.91 liters of water in the water bottle.
Answer: There are the same amount of water in the water bottle as wine in the wine bottle!
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