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A company contains two workplaces A and B. The sex ratios (female ∶ male) for the workplace A, workplace B and the total company are 2 ∶ 5, 16 ∶ 25 and 12 ∶ 25. By recruiting 9000 more people where number of females and males are in the ratio 2 ∶ 7, the sex ratio of the company changes to 19 ∶ 41. Then what is the total number of female employees working in workplace B?

A company contains two workplaces A and B. The sex ratios (female ∶ male) for the workplace A, workplace B and the total company are 2 ∶ 5, 16 ∶ 25 and 12 ∶ 25. By recruiting 9000 more people where number of females and males are in the ratio 2 ∶ 7, the sex ratio of the company changes to 19 ∶ 41. Then what is the total number of female employees working in workplace B? Correct Answer 16000

Let the number of female employees and male employees in workplace A be 2x and 5x respectively

Let the number of female employees and male employees in workplace B be 16y and 25y respectively

Total number of male employees = 5x + 25y

Total number of female employees = 2x + 16y

Total company’s sex ratio = 12/25

⇒ (2x + 16y)/(5x + 25y) = 12/25

⇒ (x + 8y)/(x + 5y) = 6/5

⇒ 5x + 40y = 6x + 30y

⇒ 10y = x

Now 9000 people are recruited with female and male ratio = 2 ∶ 7

∴ Number of male employees recruited = 7/9 × 9000 = 7000

Number of female employees recruited = 2000

New sex ratio = 19/41

⇒ (2x + 16y + 2000)/(5x + 25y + 7000) = 126/271

Substituting x = 10y

⇒ (36y + 2000)/(75y + 7000) = 19/41

Cross multiplying

⇒ 1476y + 82000 = 1425y + 133000

⇒ 51y = 51000

∴ y = 1000

Number of female employee in workplace B = 16y = 16000

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