The average age of consisting doctors and lawyers is 40. If the doctor

1.	The average age of consisting doctors and lawyers is 40. If the doctors average age is 35 and the lawyers average age is 50, find the ratio of the number of doctors to the number of lawyers.
Answer» Let the number of doctors = x Number of lawyers = y The average age of doctors = 35 The total age of doctors = 35 × x = 35 x years The average age of lawyers = 50 ∴ The total age of lawyers = 50 x y = 50y According to the sum \(\frac{35x\,\times\,50y}{x\,+\,y}\) = 40 ⇒ 35x + 50y = 40x + 40y ⇒ 40x – 35x = 50y – 40y ⇒ 5x = 10y ⇒ x/y = 10/5 (or) x : y = 2 : 1 ∴ The ratio of number of doctors to lawyers = 2:1

The average age of consisting doctors and lawyers is 40. If the doctors average age is 35 and the lawyers average age is 50, find the ratio of the number of doctors to the number of lawyers.

Answer»

Let the number of doctors = x

Number of lawyers = y

The average age of doctors = 35

The total age of doctors = 35 × x = 35 x years

The average age of lawyers = 50

∴ The total age of lawyers = 50 x y = 50y

According to the sum

\(\frac{35x\,\times\,50y}{x\,+\,y}\) = 40

⇒ 35x + 50y = 40x + 40y

⇒ 40x – 35x = 50y – 40y

⇒ 5x = 10y

⇒ x/y = 10/5

(or)

x : y = 2 : 1

∴ The ratio of number of doctors to lawyers = 2:1