Question #f0641

1 Answer
Mar 10, 2017

Answer:

Original number: #color(green)(45)#

Explanation:

If #a# is the tens digit and #b# is the units digit.
The original number is #10a+b#
and the number with the digits reversed is #10b+a#

Since the number with the digits reversed is #9# more than the original number:
#(10b+a) -(10a+b)=9#

#rarr 9b-9a=9#

#rarr b-a=1#

#rarr a=b-1#

We are also told that
#a+b=9 rarr a=9-b#

So
#b-1=9-b#

#rarr 2b=10#

#rarr b=5#

and since #a=9-b#
#rarr a=4#