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) \(\frac{1}{5}\)

Hi gsingh0711,
Kindly allow us to solve your posted questions.
You may post the official explanation later.

Anticipating your kind co-operation.
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Men = 40% of total population

Hence,
Women = 60% of total population

Now 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.
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Done. Thank you.
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