word problem for experts

Question

two vessels contain mixture of milk and water in the ratio 5:2 and 3:1 respectively. the ratio of milk and water in the new solution if two mixtures are mixed in equal amt

 

why dont we add
5/7+2/7 and 3/4+1/4
i know it will give me 1 answer i want perfect reson

why we add

5/7+3/4 =41/28

 

2/7+1/4=15/28

Answer 1

Look at it from the point of view of how much milk there is. 

 

In the first vessel 5/7 of the liquid is milk.  In the second vessel, 3/4 is milk.

 

Now we add an equal amount from each vessel.  Suppose we say, for the sake of argument, that 1 quart comes from each vessel.  So 5/7 quart of milk comes from the first vessel, and 3/4 quart of milk comes from the second.  Add those together and you get 41/28 quart of milk.  But there's a total of 2 quarts of liquid, so the actual fraction that is milk is 41/28 divided by 2, or 41/56.

 

That means that the rest, 15/56 is water.  So the ratio of milk to water in the new solution is 41/56:15/56, or 41:15.

 

And the same is true no matter what the actual amounts are, quarts, gallons, liters, or whatever.  As long as an equal amount is added from each vessel, the result would be the same.