Question

the sum of a 2 digitbno. 10 d we reverse the digits the New no. Will be 54 more than original no. what the original no.

Answer 1

Let the unit digit be x
and tens digit be y

x + y = 10

x = 10 - y ..... ( i )

10x + y = 10y + x + 54

10x - x + y - 10y = 54

9x - 9y = 54

x - y = 6 .... ( ii )


Putting value of ( i ) in ( ii )

x - y = 6

10 - y - y = 6

- 2y = - 4

y = 2

Putting in ( i )

x = 10 - y

x = 8

Original number :- 10y + x

The required number is 28

Answer 2

let the digit at units and tenths place be X and 10-x respectively for the original number
then original number =(10-x)*10+x =>100-9x
reversed number=10x+10-x =>9x+10
as per the question,
100-9x+54=9x+10
18x=144
or X=8
original number=82