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Taller and Heavier (Posted on 2013-12-06) Difficulty: 2 of 5
In a certain island, there are precisely 1000 married couples.
  1. Two thirds of the husbands who are taller than their wives are also heavier and:
  2. Three quarters of the husbands who are heavier than their wives are also taller.
If there are 120 wives who are taller and heavier than their husbands, how many husbands are taller and heavier than their wives?

No Solution Yet Submitted by K Sengupta    
Rating: 2.5000 (2 votes)

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Solution Solution Comment 2 of 2 |

If we solve by sets suppose total husbands 1000 is represented by a rectangle with two intersecting circles in it one representing husbands heavier than wife Lets say Y and one circle representing husbands taller than wife X. Then 3/4Y=2/3X=Z (Intersection of two circles) husbands which are taller and heavier than wifes.

so 120+X+Y-Z=1000 substituting for X and Z as Y we get Y=640

then X=720 so Z= 480. 

  Posted by Salil on 2013-12-11 03:51:55
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