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A team of Doctors and Nurses sent in an epidemic in the ratio of 3 ∶ 7. While treating them 12 Doctors and 60 nurses also died due to epidemic. The new ratio of doctors to nurses became 3 ∶ 5. What are the number of nurses after an epidemic?

A team of Doctors and Nurses sent in an epidemic in the ratio of 3 ∶ 7. While treating them 12 Doctors and 60 nurses also died due to epidemic. The new ratio of doctors to nurses became 3 ∶ 5. What are the number of nurses after an epidemic? Correct Answer 80

Given∶

Ratio of Doctors to Nurses = 3 ∶ 7

During epidemic, 12 doctors and 60 Nurses died

New ratio = 3 ∶ 5

Formula Used∶

If a ∶ b ∶∶ c ∶ d

product of Extremes = Product of Means

Calculation∶

Given ratio of doctors to nurses = 3 ∶ 7

Let the number of doctors be 3x and 7x

During Epidemic, 12 doctors and 60 nurses were died.

New ratio = 3 ∶ 5

According to question, the ratio will become

(3x – 12) ∶ (7x – 60) = 3 ∶ 5

⇒ 15x – 60 = 21x – 180

⇒ 21x – 15x = 180 - 60

⇒ 6x = 120

⇒ x = 20

Required number of nurses = 7x – 60 = 7 × 20 - 60 = 140 - 60 = 80

∴ 80 nurses left after an epidemic.

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