Question

the average age of three men is 50 years and their ages are in the proportion 3:5:7.The age of the youngest man is​

Answer 1

Answer:

let ages of 3 person be 3x, 5x, 7x

the average ages of three men = 50 years

according to question:-

average ages of 3 person= 3x + 5x +7x/ 3

50= 15x/3

X = 50 × 3/15

X = 10

therefore,

ages of three men are :-

3×10=30

5×10=50

7×10=70

Answer 2

Average age of three men is 50.

How to find average age?

In above question we have given that average of age of there men means sum of ages of three men. Total number of men is three.

Therefore,

Average age is the ratio of sum of ages of three men divide by three. (as there are total three men)

Let first man be M1, second man be M2 and third man be M3.

$\sf{\dfrac{M1\:+\:M2\:+\:M3}{3}}$

Also we have given that, ages of three men are in the proportion 3:5:7.

Let their ages be x.

$\implies\:\sf{M1\:=\:3x}$

$\implies\:\sf{M2\:=\:5x}$

$\implies\:\sf{M3\:=\:7x}$

Now, substitute these values in the above formula

$\rightarrow\:\sf{\dfrac{3x\:+\:5x\:+\:7x}{3}\:=\:50}$

$\rightarrow\:\sf{\dfrac{15x}{3}\:=\:50}$

$\rightarrow\:\sf{ \cancel\dfrac{15x}{3}\:=\:50}$

$\rightarrow\:\sf{5x\:=\:50}$

$\rightarrow\:\sf{x\:=\:\cancel \dfrac{50}{5}}$

$\rightarrow\:\sf{x\:=\:10}$

Therefore,

Age of first man = 3x

⇒ 3(10) = 30 years

Age of second man = 5x

⇒ 5(10) = 50 years

Age of third man = 7x

⇒ 7(10) = 70 years

We have to find the age of youngest man.

From above it's clear that first man is the younger in all.

•°• Age of the youngest man is 30 years.