Question

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 in direct proportions

Answer 1

Let , number of doctors= x
number of lawyers= y

According to Question,

〈Sum of age of x doctors 〉 ÷ x = 35
〈Sum of age of x doctors 〉 = 35x

〈Sum of age of y lawyers 〉 ÷ y = 50
〈Sum of age of y lawyers 〉 = 50y

[(sum of age of x doctors) + (sum of age of y lawyers)] ÷ ( x+y) = 40

(35x+50y) ÷ (x+y) = 40

35x+50y = 40(x+y)

35x+50y = 40x +40y

50y-40y=40x-35x

10y=5x

2y=1x

2/1 = x/y

x : y = 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 doctors be x and the number of lawyers be y.

The doctors average age is 35. So, the total age of doctors is 35x.

The lawyers average age is 50. So, the total age of lawyers is 50y.

The age of doctors and lawyers is

$T=35x+50y$

The total number of doctors and lawyers is

$N=x+y$

The average age of consisting doctors and lawyers is

$A=\frac{T}{N}$

The average age of consisting doctors and lawyers is 40.

$40=\frac{35x+50y}{x+y}$

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

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

$5x=10y$

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

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

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