Question

Students of a class are arranged in rows and columns. If there are 5 less rows, then there are 10 more number of columns formed and if there are 5 more rows, then number of columns formed are reduced by 5. The total number of students in the class are

Answer 1

Step-by-step explanation:

ANSWER

Let the number of rows be x rows and the number of students in each row be y students .

Then the total number of students in a class =xy students.

∴ According to the question , 

(x−2)(y+1)=xy⇒xy+x−2y−2=xyx−2y=2⟶(i)

And 

(x+3)(y−1)=xy⇒xy−x+3y−3=xy−x+3y=3⟶(ii)x−2y=2−x+3y=3

On adding , y=5 students.

putting the value of y in equation ⟶(i)

x−2(5)=2x=12 rows.

∴ Total number of students in a classroom =(12×5)students =60 students.

Answer 2

Concept:

Students of a class are sitting in rows and columns.

Given:

Students of a class are arranged in rows and columns. If there are 5 fewer rows, then there are 10 more columns formed and if there are 5 more rows, then the number of columns formed is reduced by 5.

Find:

The total number of students in class.

Solution:

Let's assume that number of rows= R

Number of coloums= C

According to the first condition, we can form an equation

Total number of students RC = (R - 5) (C + 10)

                                          RC = RC  - 5C + 10R  - 50

                                           10R - 5C = 50

                                                  2R- C= 10............... Eq-1

According to the second condition, we can form an equation

Total number of students RC = (R + 5) (C - 5)

                                          RC = RC  + 5C - 5R  - 25        

                                                5C - 5R = 25

                                                   C - R  = 5..................Eq2  

Add Eq1 and Eq2:

R= 15 and C= 20

So, RC= 15 X 20

          = 300

Hence, the total number of students is 300 in the class.

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