Question

2. The number of students in two classes are in ratio
2:3. If 12 students increased in each class this ratio
changes to 8:11 the total number of students in
both classes previously is​

Answer 1

Step-by-step explanation:

the no. of students in two class is in ratio 2:3

the no of students =. 2x, 3x

if 12 students increase in each class then no. of students = 2x + 12 , 3x + 12

given , 2x + 12 = 8x , 3x + 12 = 11x

therefore, 2x + 12 = 8x

12 = 8x - 2x.

12 = 6x

x = 12/6 = 2

since , x = 2

the total no. of students previously in both classes is = 2x + 3x = 2*2 + 3*2 = 4 + 6 = 10

Answer 2

Total Students = 90

Step-by-step explanation:

Given:

• Ratio of number of students in two classes are 2 : 3.
• After increasing 12 students to each class ratio becomes 8 : 11.

To Find:

• What is the total number of students in both classes previously ?

Solution: Let x be the common in given ratios. Therefore,

Ratio of students in each class = 2x and 3x

[ Now 12 students increased in both the classes ]

• Class¹ = (2x + 12) students
• Class² = (3x + 12) students

A/q

• After increasing 12 students to each class ratio becomes 8 : 11.

Let y be the common in ratios after the students increased.

So, Ratio = 8y and 11y

∴ 2x + 12 = 8y and 3x + 12 = 11y

Now let's solve the both

$\implies{\rm }$ 2x + 12 = 8y

$\implies{\rm }$ 2x = 8y – 12

$\implies{\rm }$ x = (8y – 12/2).....(1)

and

$\implies{\rm }$ 3x + 12 = 11y

$\implies{\rm }$ 3(8y – 12/2) + 12 = 11y

$\implies{\rm }$ 24y – 36/2 + 12 = 11y

$\implies{\rm }$ 24y – 36 + 24/2 = 11y

$\implies{\rm }$ 24y – 12 = 22y

$\implies{\rm }$ 24y – 22y = 12

$\implies{\rm }$ 2y = 12

$\implies{\rm }$ y = 6

Now putting the value of y in equation 1.

x = 8(6) – 12/2

x = 48 – 12/2

x = 36/2

x = 18

So number of studens in each class were

2x = 2(18) = 36 students

3x = 3(18) = 54 students

Total students = 36 + 54 = 90 students

[ For Verification ]

Ratio was 2 : 3

➮ 36/54 = 2/3 or 2 : 3 { cut by 18 }

and after increasing 12 students ratio was 8 : 11

➮ 36 + 12/54 + 12

➮ 48/66 { cut by 2 }

➮ 24/33 { cut by 3 }

➮ 8/11 or 8 : 11

$\large\bold{\texttt {Verified }}$