Question

The average age of a class of 60 students is
12 years. If the number of girls is increased
by 3/4th and the number of boys is decreased
by half, the total number of students does
not change; nor does the average age of either
the boys or the girls change. But the combined
average age changes to 13.5 years. The
average age of the boys is​

Answer 1

Answer: Average age of the boys is​ 10 years

Step-by-step explanation:

The average age of a class of 60 students is

12 years. If the number of girls is increased

by 3/4th and the number of boys is decreased

by half, the total number of students does

not change; nor does the average age of either

the boys or the girls change. But the combined

average age changes to 13.5 years. The

average age of the boys is​

the average age of students are 12 years in 60 student..

Solution:-

Given the average of class of 60 is 12years.

Also assuming the number of girls is x then the number of boys is 60-x as the total number of students is 60.

Now,

3/4th and the number of boys is decreased

by half:-

Writing and solving the above statement:-

x+(3/4)*x+(60-x)/2=60. writing the equation in variable form and solving it.

So, We say:-

(7/4)*x+(60-x)/2=60

(7/2)*x+(60-x)=120,

7x+120-2x=240,

5x=120,

So x=24.

This implies the number of students who are girls in the class is 24 and the boys is 60-24=36 boys.

Now getting the average of boys:-

Assuming average of boys is years yrs and of girls is z years.

Now,

Total sum of ages is average into number of students so:-

1) 60*12=24*z+36*y and,

2) (13.5)*60=18*y+42*z,

Solving both the equations simultaneous for z and y we get:-

1)60=2z+3y and

2)135=3y+7z solving them simultaneously:-

Subtract both to get z:-

75=5z so,

z=15 years. and the average of boys is y = 10years.

Answer:- The average age among boys is 10 years.

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Answer 2

Answer:

The average age among boys is 10 years.

Step-by-step explanation:

As per the data given,

We have to find out the average age of the boys

According to given question,

It is given that,

The average age of a class of 60 students is 12 years

If the number of girls is increased by 3/4th and the number of boys is decreased by half, the total number of students does not change; nor does the average age of either the boys or the girls change.. But the combined average age changes to 13.5 years.

Now, assuming the number of girls is x. Thus the number of boys is 60-x as the total number of students is 60.

it is given that 3/4th and the number of boys is decreased by half:-

by solving the above statement we get:-

x+($\frac{3}{4}$)*x+$\frac{60-x}{2}$=60.

Now, further solving the equation:

($\frac{7}{4}$)*x+$\frac{60-x}{2}$=60

($\frac{7}{2}$)*x+(60-x)=120,

7x+120-2x=240,

5x=120,

So x=24.

This shows that the number of students who are girls in the class is 24 and the boys is 60-24=36 boys.

Now calculating  the average of boys:-

Assuming average of boys is y yrs and of girls is z years.

Now,

Total sum of ages is average into number of students so:-

1) 60*12=24*z+36*y and,

2) (13.5)*60=18*y+42*z,

Solving both the equations simultaneous for z and y we get:-

1)60=2z+3y and

2)135=3y+7z solving them simultaneously:-

Subtract both to get z:-

75=5z so,

z=15 years. and the average of boys is y = 10years.

Hence the average age among boys is 10 years.

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