Question

In a two-digits number, the digit at ten’s place is double the digit at unit’s place. If the digits of the number are interchanged, the new number so formed is 27 less than the original number. Find the original number.

Answer 1

Hey mate !!

Here's the answer !!

Let the unit digit's place be ' x ' and ten's digit place be ' y '.

Given :-

1. y = 2x

=> The number is 10y + x

2. If the digits are interchanged, the new number formed is 10y + x - 27

To find :

10y + x = ?

Proof :

Let the interchanged number be 10x + y

=> 10y + x - 27 = 10x + y

= 10y - y + x - 10x = 27

= 9y - 9x = 27

=> y - x = 3     -----( Eqn. 1 )

Also,

= y = 2x 

=> 2x - y = 0     -----( Eqn. 2 )

Solving ( 1 ) and ( 2 ) we get,

                  y  -  x  = 3
                 -y + 2x = 0
                 _________
 
                         x = 3
                  _________

=> y = 2x 

= 2 * 3 = 6

Hence the original number is,

10y + x = 10 ( 6 ) + 3

= 60 + 3

= 63

Hence the number is 63.

Hope my answer helped you !!

Cheers !!