Question

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Answer 1

$\large\red{\underline{\underline{\bf{\blue{Question}}}}}$

The sum of the digits of a 2-digit number is 13.If the number obtained by interchanging the digits exceeds the ,original number by 27.

$\large\red{\underline{\underline{\bf{\blue{To Find}}}}}$

• Original number

• Reversed number

$\large\red{\underline{\underline{\bf{\blue{Solution}}}}}$

Let the digit at tens place be 'x'

And at Ones place be 'y'

✑ According to 1st Condition, We get,

➨ x + y = 13.

➨ x = 13 - y ----(1)

Now, Let the

Original Number = 10x + y

When digits interchanged, then

Reversed Number = 10y + x

✑ According to 2nd Condition, We get,

➨ (10y + x) + 27 = (10x + y)

➨ 10y - y + x - 10x = -27

➨ 9y - 9x = -27

➨ -9(-y + x) = -27

➨ x - y = -27/-9 = 3

➨ x - y = 3. ---(2)

Put the value of x from (1) , We get,

➨ (13 - y) - y = 3

➨ -2y = 3-13

➨ -2y = -10

➨ y = -10/-2 = 5

Put this value of y in (1)

➨ x = 13 - y

➨ 13 - 5 = 8

Hence,

${\underline{\boxed{\bf{Original\:number = 10x + y = 85}}}}$

${\underline{\boxed{\bf{Reversed Number = 10y + x= 58}}}}$

Answer 2

Answer:

ʟᴇᴛ ᴛʜᴇ ᴛᴇɴs ᴅɪɢɪᴛ ᴏғ ᴀ ʀᴇǫᴜɪʀᴇᴅ ɴᴜᴍʙᴇʀ ʙᴇ x ᴀɴᴅᴛʜᴇ ᴜɴɪᴛ ᴅɪɢɪᴛs ʙᴇ Y ᴛʜᴇɴ

Step-by-step explanation:

x+ʏ=13.......1

ʀᴇǫᴜɪʀᴇᴅ ɴᴜᴍʙᴇʀ (10X+ʏ)

ɴᴜᴍʙᴇʀ ᴏʙᴛᴀɪɴᴇᴅ ᴏɴ ʀᴇᴠᴇʀsɪɴɢ ᴛʜᴇ ᴅɪɢɪᴛs(10ʏ+x)

ᴛʜᴇʀᴇғᴏʀᴇ

(10ʏ+x) -(10x+ʏ)=27

9Y-9x=27

(ᴅɪᴠɪᴅᴇ ʙᴏᴛʜ sɪᴅᴇs ʙʏ 3)

x-ʏ =9........2

ᴏɴ ᴀᴅᴅɪɴɢ ʙᴏᴛʜ sɪᴅᴇs ᴡᴇ ɢᴇᴛ

x+ʏ =13

x-ʏ=9

2ʏ=22

x=11

sᴜʙᴛʀᴀᴄᴛɪɴɢ 11ʙʏ ᴛʜᴇ sᴜᴍ ᴏғ ᴛʜᴇ ᴅɪɢɪᴛs ᴏғ ᴛᴡᴏ ᴅɪɢɪᴛ ɴᴜᴍʙᴇʀ i.e =13

• ᴛʜᴇʀᴇғᴏʀᴇ 13-11 =2

ɪ ʜᴏᴘᴇ ᴛʜɪs ᴍᴀʏ ʜᴇʟᴘ ʏᴏᴜ