Question

A number consists of two digits whose sum of digits is 8.If 18 is added to the number, the digits interchange their places.Find the number.​

Answer 1

GiveN :

• A number consists of two digits whose sum of digits is 8.
• If 18 is added to the number, the digits interchange their places.

AnsWer :

35.

To FinD :

Find the number.

SolutioN :

Let,

• The ten digit place be x.
• unit digit be y.
• Original number ( 10x + y )
• Reversing number ( 10y + x )

☛ Case 1.

• A number consists of two digits whose sum of digits is 8.

→ x + y = 8. ____ ( 1 )

$\rule{200}2$

☛ Case 2.

• If 18 is added to the number, the digits interchange their places.

→ 10x + y + 18 = 10y + x.

→ 9x - 9y = - 18.

→ x - y = 2. ____( 2 )

✎ Now, By Elimination Methods ( Provide above ↑ )

→ 2x = 6.

→ x = 3.

✎ Putting the value of x in Equation ( 1 )

→ x + y = 8.

→ 3 + y = 8.

→ y = 5.

✡ Number become ( 10x + y ) = 10 ( 3 ) + 5 = 35.