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# chk this . is it right?

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1. 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?Answer is 330Number husbands taller than wife = xNumber husbands heavier than wife = yNumber of husbands taller and heaview =z2/3*x=z=3/4*yx=3/2 zy=4/3 zx+y-z+120=1000(3/2+4/3-1)z=1000 -120=860z=3/8*880=330

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Dear Harry

3/2+4/3-1 is 11/6 not 8/3.

Solution according to me :

Let x be the number of husbands who are taller than their wives.

Then 2/3x is the number of husbands who are taller and heavier than their wives.

Let y be the number of husbands who are heavier than their wives.

Then 3/4y is the number of husbands who are heavier and taller than their wives.

Hence,

2/3x = 3/4y:

Therefore,

x = 9/8y.

Of the 1000 husbands,

1/3x = 3/8y is the number that are taller but lighter than their wives,

1/4y is the number that are heavier but shorter than their wives,

3/4 y is the number that are heavier and taller,

and 120 is the number that are lighter and shorter.

Therefore,

3/8y + 1/4y + 3/4y + 120 = 1000

or

11/8y = 880.

This means that y = 640.

Thus,

(3/4)*640 = 480 is the number of husbands who are taller and heavier than their wives.

thanks

avi

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