Question

- The students of a class are made to stand in rows. If 3 students are extra in a row, there
would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the
number of students in the class.​

Answer 1

Step-by-step explanation:

Let the number of rows be x

Number of students in 1 row = y

According to the question,

(y + 3) (x - 1) = xy  xy + 3x - y - 3 = xy

Or 3x - y = 3 ...(1)

(y - 3) (x + 2) = xy  xy - 3x + 2y - 6 = xy

Or -3x + 2y = 6 ...(2)

Adding (1) and (2), we get,

y = 9

3x - 9 = 3  x = 4

 Number of students = xy = 4  9 = 36

Answer 2

ʜᴇʏᴀ ᴍᴀᴛᴇ!!

ʜᴇʀᴇ ɪs ᴜʀ ᴀɴsᴡᴇʀ ⏬ ⏬

sᴏʟᴜᴛɪᴏɴ:

ʟᴇᴛ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ ʀᴏᴡs ʙᴇ ʏ ᴀɴᴅ ɴᴜᴍʙᴇʀ ᴏғ sᴛᴜᴅᴇɴᴛs ɪɴ ᴀ ʀᴏᴡ ʙᴇ x.

ᴛᴏᴛᴀʟ sᴛᴜᴅᴇɴᴛs ᴏғ ᴛʜᴇ ᴄʟᴀss= ɴᴜᴍʙᴇʀ ᴏғ ʀᴏᴡs × ɴᴜᴍʙᴇʀ ᴏғ sᴛᴜᴅᴇɴᴛs ɪɴ ᴀ ʀᴏᴡ

ᴛᴏᴛᴀʟ sᴛᴜᴅᴇɴᴛs ᴏғ ᴛʜᴇ ᴄʟᴀss= xʏ

ᴄᴏɴᴅɪᴛɪᴏɴ ɪ

ᴛᴏᴛᴀʟ ɴᴜᴍʙᴇʀ ᴏғ sᴛᴜᴅᴇɴᴛs = (ʏ -1) (x +3)

xʏ = (ʏ-1) (x+ 3)

xʏ= xʏ - x + 3ʏ-3

3ʏ − x-3 = 0

3ʏ − x= 3

-x+3ʏ=3…………,...(1)

ᴄᴏɴᴅɪᴛɪᴏɴ ɪɪ:

ᴛᴏᴛᴀʟ ɴᴜᴍʙᴇʀ ᴏғ sᴛᴜᴅᴇɴᴛs = (ʏ + 2) (x− 3)

xʏ = xʏ + 2x-3ʏ− 6

2x− 3ʏ = 6………….. (2)

ᴏɴ ᴍᴜʟᴛɪᴘʟʏɪɴɢ ᴇϙᴜᴀᴛɪᴏɴ (1) ʙʏ (2)

2(-x+3ʏ=3)

-2x+6ʏ=6……………….(3)

ᴏɴ ᴀᴅᴅɪɴɢ ᴇϙᴜᴀᴛɪᴏɴ 2 ᴀɴᴅ 3

2x− 3ʏ = 6

-2x+6ʏ=6

--------------------

3ʏ=12

ʏ=12/3

ʏ=4

ᴏɴ ᴘᴜᴛᴛɪɴɢ ʏ= 4 ɪɴ ᴇϙ 1.

-x+3ʏ=3

-x+3(4)=3

-x+12=3

-x=3-12

-x=-9

x=9

ɴᴜᴍʙᴇʀ ᴏғ sᴛᴜᴅᴇɴᴛs ɪɴ ᴄʟᴀss= xʏ=9×4=36.

ʜᴇɴᴄᴇ, ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ sᴛᴜᴅᴇɴᴛs ɪɴ ᴄʟᴀss=36