Question

the sum of the digits of a two-digit number is 8 and the difference between the number and the formed by reversing the digits is 18 find the number​

Answer 1

Given :

• The sum of digits of a two digit is 8.
• The difference between the number and that formed by reversing the digits 18.

To find :

• what is the number ?

Solution :-

• Let the digit at unit's place be x .
• the digit at ten 's place b y

then,

Number = 10y + x

Number formed by reversing the digits = 10y + x

___________________

According to the given conditions ,

so,

⇒ x + y = 8 ..... ( eq 1 )

And ,

⇒ ( 10 y + x ) - (10x + y ) = 18

⇒ 9 ( y - x ) = 18

⇒ y - x = 2 ....... ( eq 2 )

➤ Add both the equations we get ,

⇒ x + y + x - y = 8 + 2

⇒ 2x = 10

⇒ x = 10/2

⇒ x ↠5

➤ Putting the value of x in equation (ii)

⇒ x - y = 2

⇒ 5 - y = 2

⇒ y = 5 - 2

⇒ y ↠ 3

hence,

➤ Tens digit = x ↠ 5

➤ Ones digit = y ↠ 3

Therefore,

➤ Original number = 10x + y ↠ $53$

➤ Reversed number = 10y + x ↠ $<strong>35</strong>$

______________________

Answer 2

Answer:

Let the digit at unit's place be x .

the digit at ten 's place b y

then,

Number = 10y + x

Number formed by reversing the digits = 10y + x

___________________

According to the given conditions ,

so,

⇒ x + y = 8 ..... ( eq 1 )

And ,

⇒ ( 10 y + x ) - (10x + y ) = 18

⇒ 9 ( y - x ) = 18

⇒ y - x = 2 ....... ( eq 2 )

➤ Add both the equations we get ,

⇒ x + y + x - y = 8 + 2

⇒ 2x = 10

⇒ x = 10/2

⇒ x ↠5

➤ Putting the value of x in equation (ii)

⇒ x - y = 2

⇒ 5 - y = 2

⇒ y = 5 - 2

⇒ y ↠ 3

hence,

➤ Tens digit = x ↠ 5

➤ Ones digit = y ↠ 3

Therefore,

➤ Original number = 10x + y ↠ 5353

➤ Reversed number = 10y + x ↠ 3535

Step-by-step explanation:

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