Question

The difference of the two digits of a number is 3. If this number is added to the number obtained
by interchanging the digits, the sum is 99. What is the number


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Answer 1

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

The difference of the two digits of a number is 3.

x - y = 3 ....... ( i )

If this number is added to the number obtained by interchanging the digits, the sum is 99.

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

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

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

The number

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

According to the Problem,

⇒ 10x + y + 10y + x = 99

⇒ 11x + 11y = 99

⇒ 11( x + y ) = 99

⇒ x + y = 9 ....... ( ii )

Adding eq ( i ) and eq ( ii ),

x + y = 9

x - y = 3

____________________

2x = 12

⇒ x = 6

Substituting value of x in eq ( ii ),

x + y = 9

⇒ 6 + y = 9

⇒ y = 9 - 6

⇒ y = 3

•°• The Number = 10x + y

= 10 × 6 + 3

= 63

$<b><u>•°• The Required Number = 63 </u></b>$