Question

THE TOTAL NUMBER OF STUDENTS IN SECTION A & B OF CLASS IS 72.THE RATIO OF NUMBER OF STUDENTS A & B IS 7:5.THE AVERAGE WEIGHT OF STUDENTS OF STUDENTS IN SECTION B IS 20% MORE THAN THAT OF THE STUDENTS IN SECTION A.IF THE AVERAGE WEIGHT OF ALL STUDENTS IN CLASS IS 52 KG.WHAT IS AVERAGE WEIGHT OF SECTION B.​

Answer 1

Answer:

Let the number of students in Section A and B be, 7x and 5x respectively.

We know,

7x+5x=72

=>12x=72

=>x=6

Then 7x=42 and 5x=30

Let sum of weights of all students in sec. a be, a and sec. b be, b.

Now average weight of students of

Section A=a/42

Section B=b/30

We are given that,

a/42+20% of a/42= b/30

=>a/42+ a/210=b/30

=>6a/210=b/30

=>a=b/30*210/6

=>a=7b/6

Now, average of all students is a+b/72

So, a+b/72=52

=>a+b=52*72

=>7b/6+b=52*72

=>13b/6=52*72

=>b=1728

Average weight of section B = b/30 = 1728/30= 57.6 kg

Answer 2

Answer:

The average weight (in $\mathrm{kg}$ ) of the students in section $B$ is $57.6$.

Step-by-step explanation:

Given:

The total numbers of students in sections $A and B$ of a class are $72 .$

The ratio of the number of students  $A and B$ is$7: 5$.

The average weight (in$\mathrm{kg}$ ) of the students in section B is $20 \%$more than that of the students in the section $\mathrm{A}$.

The average weight of all the students in the class is $52 \mathrm{~kg}$,

Formula used:

The average $=$ sum of observations $/$ Number of observations

Calculation:

The number of students $=72$

Number of students in section $A=72 \times(7 / 12)=42$

Number of students in section $B=72-42=30$

Let the average weight of section $A be 5 x$

Average weight of the section $B=5 x \times(6 / 5)=6 x$

According to the question

$\begin{aligned}&42 \times 5 x+30 \times 6 x=72 \times 52 \\&210 x+180 x=3744 \\&390 x=3744 \\&x=3744 / 390=9.6\end{aligned}$

Average weight of students in section $B=6 x=6 \times 9.6=57.6$

$\therefore$ The average weight (in $\mathrm{kg}$ ) of the students in section $B$ is $57.6$.

Alternate Solution:

Let the number of students in sections $A and B$are 7 and 5 respectively.

Let the average weight of section $A be 5 x .$

Average weight of section$B=5 x \times(6 / 5)=6 x$

According to the question

$\begin{aligned}&7 \times 5 x+5 \times 6 x=12 \times 52 \\&35 x+30 x=12 \times 52 \\&65 x=12 \times 52 \\&x=(12 \times 52) / 65=9.6\end{aligned}$

Hence The average weight (in $\mathrm{kg}$ ) of the students in section $B$ is $57.6$.