Question

There are 100 students in a class. The mean ages of boys and girls are 14.2 yrs and 13.2 yrs. If boys and girls are combined together, then mean age is 13.6 yrs. What percent of students in the class constitutes of boys?

Answer 1

Answer:

      40%

Step-by-step explanation:

Let b be the number of boys.

Then the number of girls is g = 100 - b.

The mean age of boys is 14.2

   ⇒  the sum of the ages of boys if 14.2b.

The mean age of girls is 13.2

   ⇒  the sum of the ages of girls is 13.2g = 13.2(100 - b) = 1320 - 13.2b

So the sum of the ages of all students is:

   14.2b + 1320 - 13.2b = 1320 + b

The mean age of all students is 13.6

   ⇒ (1320 + b) / 100 = 13.6

   ⇒ 1320 + b = 1360

   ⇒  b = 1360 - 1320 = 40

So 40 of the 100 students are boys.

As a percentage, that is 40%.