Question

in a certain examination, the average grade of all students in class A is 68.4 and the students in class B is 71.2 . if the average if both classes cimbined is 70 , find the ratio of the number of students in class A ro the number of students in class B.​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

The ratio of the number of students is 3:4

Solution:

Given Data:

Class A =$n_{1}$

Class B = $n_{2}$

Step-by-step explanation:

Step 1:

Average marks of class A = 68.4

Sum of the marks of all the students in class A/number of students in class A = 68.4

Step 2:

Sum of the marks of all the students in class A = 68.4 $n_{1}$   .....(1)

Step 3:

Average marks of class B =71.2

⇒sum of the marks of all the students in class B number of students in class B = 71.2

Step 4:

⇒ sum of the marks of all the students in class B $n_{2}$ = 71.

Sum of the marks of all the students in class B = 71.2 $n_{2}$ ........(2)

Let average marks of both classes = 70

Step 5:

⇒sum of the marks of all the students in class A + sum of the marks of all the students in class $\frac{B}{n_{1}}+n_{2}=70$

$\Rightarrow 68.4 n_{1}+71.2 \frac{n_{2}}{n_{1}}+n_{2}=70$

Step 6:

$\Rightarrow 70 n_{1}+70 n_{2}=68.4 n_{1}+71.2 n_{2}$

$\Rightarrow 1.6 n_{1}=1.2 n_{2}$

Step 7:

Result:

$\Rightarrow \frac{n_{2}}{n_{1}}=\frac{1.2}{1.6}$

$=\frac{3}{4}$