Question

Difference between the digits of a two digit number is 5. Three times this number is 8

times the number obtained by interchanging the digits. Find the number.​

Answer 1

Explanation:

Let one's digit=y

Units digit=x

Number=10x+y

⇒8(10x+y)=3(10y+x)

⇒80x+8y=30y+3x

⇒77x=22y

⇒7x=2y−−−(1)

Also, x−y=5−−−(2)

from eq(1) and (2)

⇒x−y=5

                                           

⇒x+72y−y=5

⇒2y−7y=35

⇒−5y=35

⇒y=−7

⇒x−y=5

⇒x+y=5

⇒x=−2

Number=−27

or

⇒y−x=5       

                                    

⇒y−72y=5

⇒5y=35

⇒y=7

⇒7−x=5

⇒x=2

Number=27

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