In a certain community ther are 1000 married couples. Two thirds of the husbands who are taller than their wives are also heavier and 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?

Interview Candidate
Nov 26th, 2005
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cybrainx
Profile Answers by cybrainx

Dec 1st, 2005

Answer is 330
Number husbands taller than wife = x
Number husbands heavier than wife = y
Number of husbands taller and heaview =z
2/3*x=z=3/4*y
x=3/2 z
y=4/3 z
x+y-z+120=1000
(3/2+4/3-1)z=1000 -120=860
z=3/8*880=330

hridish

Feb 3rd, 2006

There is a calculation mistake.
the answer is (3/2 + 4/3 +1)z=880
z=880*6/11
z=480

kiddoo99
Profile Answers by kiddoo99

Mar 16th, 2010

There are 1000 husbands, subtracting the 120 wives who are taller and heavier leaves 880 husbands. Think Venn diagrams: 2/3T=3/4H (this is the intersection or both who are heavier and taller). Solve this for T and so T=9/8H.

880 = 1/3T + 3/4H + 1/4H

880= (1/3)(9/8H) + H

880= 11/8H

640 = H

and finally the intersection of heavier and taller is 3/4 (640) =480