Problem Solving

In a survey of X people it was found that 40% are Men and the earnings of 75% Men are greater than $75000 per annum. 2/5 of the people surveyed earned more than $75000 per annum. What fraction of the total females earn less than or equal to $75000 ?

Let X be 100.
Total number of Men surveyed = (40/100) * 100 = 40
Total number of Men(surveyed) earning more than $75000 per annum = (75/100)*40 = 30
Total number of Women surveyed = 100 - 40 = 60
Total number of people(surveyed) earning more than $75000 per annum = (2/5)*100 = 40
Total number of Women(surveyed) earning more than $75000 per annum = Total number of people(surveyed) earning more than $75000 per annum - Total number of Men(surveyed) earning more than $75000 per annum = 40 - 30 = 10.

What fraction of the total females earn less than or equal to $75000 ?
= (Total number of Women surveyed - Total number of Women(surveyed) earning more than $75000 per annum)/Total number of Women surveyed
= (60-10)/60
= 50/60
= 5/6

Let X equal 100.

So, # of men = 40 and # of women = 60

75% of men earn greater than 75000 => 30 men earn more than 75000.

Also, 2/5th of all men and women earn more than 75000 => 40 men & women earn more than 75000.

Since, out of 40 who earn more than 75k, 30 are men..therefore, 10 out of 60 women earn more than 75k.

Therefore, fraction of women who earn less than or equal to 75k = (60-10)/60 = 50/60 = 5/6.