Question

The average age of doctors and lawyers together is 40.if the doctors average age is 35 and the layers average age is 50, find the ratio of the number of doctors to the number of lawyers

Answer 1

suppose there are n doctor and m lawyers
now
total age of lawyer and doctor combine is
(n+m)×40
total age of doctors=35*n
total age of lawyers= 50×m
now
35×n+50×m=40×(n+m)
so

10m=5n
2:1

Answer 2

Answer:

The ratio of the number of doctors to the number of lawyers is 2:1.

Step-by-step explanation:

Let the number of doctor be x and the number of lawyers be y.

The average age of doctors and lawyers together is 40.

Total age of doctors and lawyers is

$\text{Total age}=40(x+y)=40x+40y$                 .... (1)

The doctors average age is 35. Total age of doctors is 35x.

The lawyers average age is 50. Total age of lawyers is 50y.

Total age of doctors and lawyers is the sum of doctors age and lawyers age.

$\text{Total age}=35x+50y$                           .... (2)

From (1) and (2), we get

$40x+40y=35x+50y$

$40x-35x=50y-40y$

$5x=10y$

$\frac{x}{y}=\frac{10}{5}$

$\frac{x}{y}=\frac{2}{1}$

Therefore the ratio of the number of doctors to the number of lawyers is 2:1.