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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:
Given the proportion of ages of three men are 3:5:7.
Let their ages be 3k, 5k, 7k ,where k is any constant.
Given average of ages of three men = 50
$$\Rightarrow \frac{3k+5k+7k}{3} = 50$$
$$\Rightarrow \frac{15k}{3} = 50$$
$$\Rightarrow 5k = 50$$
$$\Rightarrow k = 10$$
Therefore the ages of three men are 30, 50, and 70 years.
The age of the youngest men is 30 years.
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