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Who is taller and Heavier?

There is a community in which there are 1000 couples. In that 2/3rd of men who are taller are also heavier and 3/4th of the men who are heavier are also taller and there are 120 women who are both heavier and taller than men. So how many men are both taller and heavier than women?

SOLUTION : Let number of men taller than their wives be x. Let number of men heavier than their wives be y. According to question, the number of men neither heavier nor taller than their wives = 120 . Then, number of men taller and heavier than their wives = 2x/3 . And, number of men heavier and taller than their wives = 3y/4 . 2x/3 = 3y/4

Number of men taller than their wives, but not heavier = x-2x/3 = x/3 . Number of men heavier than their wives, but not taller = y-3y/4 = y/4 . Their can be 4 cases possible, men heavier than women but not taller, men taller than women but not heavier, men neither heavier nor taller or men both heavier and taller than women.

Total couples = 1000 . y/4 + x/3 + 120 + 2x/3 = 1000 . Solving the two equations we get, number of men taller and heavier than their wives = 2x/3 = 480

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