Math, asked by ananya2804, 10 months ago

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

Answers

Answered by IITGENIUS1234

$Given :-$

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.

$Let the two - digit number be 10x + y $

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

$To Find :-$

The number

$Solution :-$

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

$•°• The Required Number = 63 $

ananya2804: thanks a lot but the answer is 36 and not 63

IITGENIUS1234: no the answer is 63

IITGENIUS1234: if the answer is 36, the difference of the digits will be ( - 3 )

IITGENIUS1234: minus 3

ananya2804: okkk..

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