gsingh0711 wrote:
In a survey of X people it was found that 40% are men and the earnings of 75% of the 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?
A) \(\frac{2}{3}\)
B) \(\frac{1}{6}\)
C) \(\frac{5}{6}\)
D) \(\frac{1}{2}\)
E) \(\frac{1}{5}\)
Men = 40% of total population
Hence,
Women = 60% of total populationNow question says,
75% of the men earn greater than $75000 per annum
That means, 75% of 40% of men earn greater than $75000 per annum =
30% of all men ------ (1)
Now question also says,
\(\frac{2}{5}\) of the people surveyed earned more than $75000 per annum.
Now \(\frac{2}{5}\) of 100% =
40%
Out of the 40%, 30% are men --------- From (1)
That is
remaining 10% are women. ----- (2)
Now we need to find,
fraction of the total females earn less than or equal to $75000.
If 10% out of the 60% women earned more than $75000 per annum, then,
50% out of 60% women earned less than or equal to $75000 per annum.
that makes it \(\frac{5}{6}\)Hence C.