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

Answer:

• There are 300 students in the class .

Step-by-step explanation:

Let, number of rows = x

and number of columns = y

then,

total number of students = x y

Now,

• According to the first condition when, there are 5 less rows then, there are 10 more columns formed , so

→  ( x - 5 ) ( y + 10 ) = x y

→ x y + 10 x - 5 y - 50 = x y

→ 10 x - 5 y = 50

→ 2 x - y = 10

→ y = 2 x - 10  ... eqn (1)

• According to the second condition when, there are 5 more rows then number of columns formed are reduced by 5 , so

→ ( x + 5 ) ( y - 5 ) = x y

→ x y - 5 x + 5 y - 25 = x y

→ - 5 x + 5 y = 25

→ y - x = 5

using eqn (1)

→ 2 x - 10 - x = 5

→ x = 15

putting value of x in eqn (1)

→ y = 2 x - 10

→ y = 2 ( 15 ) - 10

→ y = 20

so,

total number of students = x y

                                            = ( 15 ) ( 20 )

                                            = 300

therefore,

There are 300 students in the class .

Answer 2

$\bf\large{\underline{Question :- }}$

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.

________________________________

$\bf\large{\underline{Solution :- }}$

→ Let,

• → r = no. of rows

• → c = no. of columns

• → X = total students

→ r × c = X

→ (r-5) x (c+10) = X

→ (r+5) × (C-5) = X

• solve these equations simultaneous ,we get

→ 10r - 5c - 50=0

→ -5r + 5c - 25=0

→ 5r = 75

→ r =1 5

→ c = 20

________________________________

$\bf\large{\underline{Therefore :- }}$

• Rows = 15
• Column = 20

• ★Total number of students in class

◆ Rows × column = 15 × 20 = 300

$\bf\large{\underline{Hence:- }}$

• Rows = 15
• Column = 20
• Total student in class = 300