Aptitude Discussion

Q. |
Forty percent of the employees of a company are men, and 75 percent of the men earn more than Rs.25,000 per year. If 45 percent of the company's employees earn more than Rs.25,000 per year, what fraction of the women employed by the company earn Rs.25,000 per year or less? |

✖ A. |
\(\dfrac{2}{11}\) |

✖ B. |
\(\dfrac{1}{4}\) |

✖ C. |
\(\dfrac{1}{3}\) |

✔ D. |
\(\dfrac{3}{4}\) |

**Solution:**

Option(**D**) is correct

Let the total number of employees be \(p\).

Number of men earning more than 25,000,

\(= 0.4 \times 0.75 \times p\)

Number of women earning more than 25,000,

\(= 0.45p - (0.4 \times 0.75 \times p)\)

Number of women employed by company \(= 0.6p\)

Number of women earning Rs.25,000 per year or less,

\(= 0.6p - (0.45p - 0.4 \times 0.75 \times p)\\ = 0.45p\)

Fraction of women earning Rs.25,000 or less,

\(=\dfrac{0.45p}{0.6p}\\ =\dfrac{3}{4}\)

**Edit:** For an alternative solution, check comment by **Sourav Bibhor.**

**Ritaprava**

*()
*

**Sourav Bibhor**

*()
*

Assume the number of employees is 100.

$40\% * 100 = 40$ men of the total employees

Now 75% of 40 = 30 men earning more than 25000.

Now,

45% of total employees is equal to the number of employees earning more than 25000,

$100*(\frac{45}{100})=30+W$

$W= 15$

Then the total number of women earning less than or equal to 25000$=60-15=45$

So, the ratio,

$=\dfrac{45}{60}$

$=\dfrac{3}{4}$

**Zoha Amjad**

*()
*

assume number of employees are 100

40% * 100 = 40 men of the total employees

now 75% of 40 = 30 men earning more than 25000

now

45% of total employees is equal to the number of employees earning more than 25000

100*(45/100)=30+W

W= 15

(15/60)*100=25

after getting 25 what is to be done??

15/60 is proportion of above ones. but they ask of below. so thats 45/60 = 3/4

what is required ? (women emp. earning