Question

there are two classrooms A and B containing students. If 5 students are shifted from Room A to B, the resulting number of students in Room A becomes double the number of students left in Room B . Find the original number.

answer: 35 , 25

please answer quickly​.

Answer 1

Let number of students in classroom A be "x" and number of students in classroom B be "y".

If 5 students are shifted from Room A to B, then

(As, 5 students arr shifted from classroom A then subtract 5 from them and in classroom B 5 added. Because students are shifted from classroom A to B)

According to question,

⇒ x - 5 = y + 5

⇒ x = 5 + 5 + y

⇒ x = 10 + y ____ (eq 1)

Also, the resulting number of students in classroom A becomes double the number of students left in Room B .

(Means, if 5 students are shifted from classroom B to A then number of students in classroom A becomes double the number of students that left classroom B)

⇒ 2(y - 5) = x + 5

⇒ 2y - 10 = x + 5

⇒ 2y - 10 = 10 + y + 5 [From (eq 1)]

⇒ 2y - 10 = 15 + y

⇒ 2y - y = 15 + 10

⇒ y = 25

Substitute value of y in (eq 1)

⇒ x = 10 + 25

⇒ x = 35

∴ Number of students in classroom A is 35 and in classroom B is 25.

Answer 2

ʟᴇᴛ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ sᴛᴜᴅᴇɴᴛs ɪɴ ᴛʜᴇ ᴄʟᴀssʀᴏᴏᴍ ᴀ ʙᴇ 'x' ᴀɴᴅ ʙ ʙᴇ 'ʏ'.

(ɪ)

ɪғ 5 sᴛᴜᴅᴇɴᴛs ᴀʀᴇ sʜɪғᴛᴇᴅ ғʀᴏᴍ ᴀ ᴛᴏ ʙ, ᴛʜᴇɴ ᴡᴇ ʜᴀᴠᴇ:

x - ⑸ = ʏ + ⑸

x - ʏ = 10

(ɪɪ)

ɪғ 5 sᴛᴜᴅᴇɴᴛs ᴀʀᴇ sʜɪғᴛᴇᴅ ғʀᴏᴍ ʙ ᴛᴏ ᴀ, ᴛʜᴇɴ ᴡᴇ ʜᴀᴠᴇ:

⇒ 2(ʏ - 5) = x + ⑸

⇒ 2ʏ - 10 = x + ⑸

⇒ x - ⑵ʏ = -15

ᴏɴ sᴏʟᴠɪɴɢ (ɪ) & (ɪɪ), ᴡᴇ ɢᴇᴛ

x - ʏ = 10

x - ⑵ʏ = -15

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

ʏ = 25

sᴜʙsᴛɪᴛᴜᴛᴇ ʏ = 25 ɪɴ (ɪ),ᴡᴇ ɢᴇᴛ

⇒ x - ʏ = 10

⇒ x - 25 = 10

⇒ x = 35

ᴛʜᴇʀᴇғᴏʀᴇ:

ɴᴜᴍʙᴇʀ ᴏғ sᴛᴜᴅᴇɴᴛs ɪɴ ʀᴏᴏᴍ ᴀ = 35

ɴᴜᴍʙᴇʀ ᴏғ sᴛᴜᴅᴇɴᴛs ɪɴ ʀᴏᴏᴍ ʙ = 25.