Question

$\huge\colorbox{pink}{Question↓ }$

The sum of the two digit number and the number obtained by interchanging the digit is 132 the digit in the tens place is 2 more than the digit in the unit place.Find the original Number.

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❍ ᴅᴏɴᴛ sᴘᴀᴍ

❍ ᴅᴏɴᴛ ʀᴇᴘᴏʀᴛ

❍ ᴀɴsᴡᴇʀ ᴡɪᴛʜ ғᴜʟʟ sᴏʟᴜᴛɪᴏɴ


Cʟᴀss- 10ᴛʜ

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ᴀʀᴍɪᴇs ᴄᴀɴ ᴀɴsᴡᴇʀ​

Answer 1

Step-by-step explanation:

$\huge\colorbox{pink}{Question↓ }$

The sum of the two digit number and the number obtained by interchanging the digit is 132 the digit in the tens place is 2 more than the digit in the unit place.Find the original Number.

$\huge\colorbox{pink}{solution↓ }$

Let unit's digit be :- y

Let ten's digit be :- x

So, the number formed will be = 10x + y

After interchanging the number we get = 10y + x

The sum of the number = 10x + y

The sum of digits = x + y

According to the question,

➙ ( 10x + y ) + ( 10y + x ) = 132

➙ 11x + 11y = 132

➙ 11 ( x + y ) = 132

➙ x + y = 12 ------ (1)

Now,

➙ 10x + y + 12 = 5( x + y )

➙ 10x + y + 12 = 5x + 5y

➙ 10x - 5x + y - 5y = -12

➙ 5x - 4y = -12 ------ (2)

From equation (1) we get,

➙ x = 12 - y ----- (3)

Putting value of 'x' from (3) in (2)

➙ 5x - 4y = -12

➙ 5( 12 - y ) - 4y = -12

➙ 60 - 5y - 4y = -12

➙ 60 + 12 = 9y

➙ 72 = 9y

➙ y =

$\frac{\cancel{72}}{\cancel{9}}$

➙ y = 8 ------ (4)

Putting value of 'y' in equation (3)

➙ x = 12 - y

➙ x = 12 - 8

➙ x = 4

So, the original number is,

✒ 10x + y

✒ 10 × 4 + 8

✒ 40 + 8

✒ 48

∴ The number is 48 .

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Hope it will be Helpful Bish -__-

Saranghe ❤️~

Answer 2

Step-by-step explanation:

Let unit’s digit = y and

the ten’s digit = x So,

the original number = 10x + y

After interchanging the digits,

New number = x + 10y

The sum of the number = 10x + y

The sum of the digit = x + y

According to the question,

(10x + y) + (x + 10y) = 132

⇒ 11x + 11y = 132

⇒ 11(x + y) = 132

⇒ x + y = 12 …(i) and

10x + y + 12 = 5(x + y)

⇒ 10x + y + 12 = 5x + 5y

⇒ 10x – 5x + y – 5y = – 12

⇒ 5x – 4y = – 12 …(ii)

From Eq. (i), we get

x = 12 – y …

(iii) On substituting the value of

x = 12 – y in Eq. (ii),

we get 5(12 – y) – 4y = – 12

⇒ 60 – 5y – 4y = – 12

⇒ – 9y = – 12 – 60

⇒ – 9y = – 72

⇒ y = 8

On putting the value of y = 8 in Eq. (iii),

we get x = 12 – 8 = 4 So,

the Original number = 10x + y = 10×4 + 8 = 48