Question

In a class, the number of boys and girls are distinct.
The average age of all the student in the class equals
the average of the average age of the boys and the
average age of the girls. The sum of the average age of
the boys and the average age of the girls is 10 years.
Find the average age (in years) of the boys of the class.
एक कक्षा में लडकी और लडकों की संख्या भिन्न-भिन्न​

Answer 1

Step-by-step explanation:

In general, in any weighted average problem, the average you get when you combine the groups will always be closer to the average of the larger group. For example, if you have men earning $40 per hour, and women earning $50 per hour at a company, then if there are more women than men at the company, the overall average wage will be closer to $50 than to $40 (so will be greater than $45). But here, we learn that the overall average age is exactly equal to the average of the average age of the boys and the average age of the girls, or in other words, it is exactly midway between them. That can only happen in one of two ways: either we have exactly equal numbers of boys and of girls, or the average age of the boys is identical to the average age of the girls. Since the question tells us the number of boys is different from the number of girls, then their average ages must be identical, and if they sum to 10, each group has an average age of 5.