Question

sum of the digit of a 2- digit number is 8 if the digit of the number reversed the number remaining the same find the number
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Answer 1

$<b><u>Given :-</u></b>$

Sum of the digit of a 2 - digit number is 8.

⇒x + y = 8 ....... ( i )

If the digits are reversed, the number remains the same.

$<b>Let the number be 10x + y</b>$

$\rule{330}{5}$

$<b><u>To Find :-</u></b>$

The number

$\rule{330}{5}$

$<b><u>Solution :-</u></b>$

When the number is reversed, the number becomes $<b>10y + x <b>$

According to the problem,

⇒ 10x + y = 10y + x

⇒ 10x + y - x - 10y = 0

⇒ 9x - 9y = 0

⇒ 9 ( x - y ) = 0

⇒ x - y = 0 ....... ( ii )

Adding eq ( i ) from eq ( ii ),

x + y = 8

x - y = 0

_____________________

2x = 8

⇒ x = 4

Substituting value of x in eq ( i ),

x + y = 8

⇒ 4 + y = 8

⇒ y = 8 - 4

⇒ y = 4

•°• The Number = 10x + y

= 10 × 4 + 4

= 44

$<b>•°• The Required Number is 44</b>$