The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.
Let us consider,
One's digit of a two digit number =x and
Then's digit =y
So, the number is x+10y
By interchanging the digits,
One's digit =y and
Ten's digit =x
Number is y+10x
As per the statement,
x+y=12.....(1)
y+10x=x+10y+18
y+10x−x−10y=18
x−y=2....(2)
Adding (1) and (2), we have
2x=14 or x=7
On subtracting (1) from (2),
2y=10 or y=5
Answer:
number =7+10×5=57