Question

4: Students of a class have been divided into two groups in the ratio 7:13. If the first group
consists of 70 students, how many students are there in the class?​

Answer 1

GIVEN:-

• Student of Class is divided into two groups.

• Ratio is 7:13.

• First Group Consist of 70 Student.

TO FIND:-

• Total number of Student in the Class.

EXPLANATION:-

Let the ratio be x and y

$\rm{First\:Group=7x}$

$\rm{Second\:Group=13y}$

Comparing the both.

$\rm{13y=7x}$

$\rm{y=\dfrac{13}{7}x}$

Atq. it is stated that First group has 70 students so x will also be 70.

Now,

$\rm{y=\dfrac{13}{\cancel{7}}\times{\cancel{70}}}$

$\rm{y=13×10=130Students}$

So, Second Group consist of 130 Student.

Now,

$\rm{x+y= Total\:Number\:of\:Student}$

$\rm{70+130=200 Student}$.

Hence, The total Number of Student is 200 Student.

VERIFICATION:-

$\rm{7x+13x=200}$

$\rm{20x=200}$

$\rm{x=\dfrac{200}{20}}$

$\rm{x=10 Student}$

First group student =7x= 7×10=70Student.

Second group Student= 13×10=130 Student.

Answer 2

Step-by-step explanation:

${\red{\underline{\underline{\bold{Given:-}}}}}$

• Students of a class are divided into two groups in the ratio 7:13

• The first group consists of 70 students

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The total number of students in the class.

${\green{\underline{\underline{\bold{Solution:-}}}}}$

Let the number of students in first group be ' x ' and second group be ' y '

Given ratio of the students in these 2 groups = 7:13

So:-

→ $\bf x : y = 7 : 13$

→ $\bf \frac{x}{y} = \frac{7}{13}$

→ $\bf\frac{70}{y} = \frac{7}{13}$

→$\bf \frac{1}{y} = \frac{7}{13} \times \frac{1}{70}$

→ $\bf \frac{1}{y} = \frac{1}{13 \times 10} = \frac{1}{130}$

→ $\bf y = 130$

So, The second group consists 130 students.

Total number of students = Number of students in first group + Number of students in second group

→ 70 + 130

$\boxed{ Total \:number\: students= 200}$