Question

1. In a certain community there are 1000 married couples. Two-thirds of the husbands who are taller than their wives are also heavier and three-fourths 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 1

Let $x=$ husbands that are both taller and heavier.

Husbands that are taller but lighter is $\dfrac{x}{2}.$

Husbands that are heavier but shorter are $\dfrac{x}{3}$ .

Then

$$x+\dfrac{x}{2}+\dfrac{x}{3}+120=1000$$

$$\dfrac{11x}{6}=880$$

$$x=\dfrac{880(6)}{11}$$

$$x=480$$

480  husbands are taller and heavier than their wives.