Question

the sum of the digits of a two-digit number is 10 if we reverse the digit the new number will be 54 more than the original number what is the original number

Answer 1

Let xy be the required two-digit number.

Let x be the number which is in unit's digit.

Let y be the number which is in ten's digit.

Therefore the decimal expansion is 10x + y.


Given that if we reverse the digit the new number will be 54 more than the orginal number.

10y + x = 10x + y + 54

-9x + 9y = 54

-x + y = 6   ------- (1)



Given that sum of the digits of a two-digit number = 10.

x + y = 10   ------ (2).



On solving (1) & (2), we get

-x + y = 6

x + y = 10

--------------

    2y = 16

      y = 8.


Substitute y = 8 in (2), we get

x + y = 10

x + 2 = 10

x = 10 - 2

x = 8.


Therefore the original number = 28.


Hope this helps!

Answer 2

the answer is in attachment. and the no.( number) is 28