Question

In a certain examination the overage grade of all the students in class 'A' is 68.4 and of students of class 'B' is 71.2. If the overage of both the classes combined is 70. Find the rotio of the number of students in class A and class B?​

Answer 1

Answer:

The ratio of the number of students is 3:4

Solution:

Given Data:

Class A =n_{1}n

1

Class B = n_{2}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}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}n

2

= 71.

Sum of the marks of all the students in class B = 71.2 n_{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

n

1

B

+n

2

=70

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

1

+71.2

n

1

n

2

+n

2

=70

Step 6:

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

1

+70n

2

=68.4n

1

+71.2n

2

\Rightarrow 1.6 n_{1}=1.2 n_{2}⇒1.6n

1

=1.2n

2

Step 7:

Result:

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

n

1

n

2

=

1.6

1.2

=\frac{3}{4}=

4

3