If 18 is added to a two-digit number, the digits are reversed. The sum of the digits is 8. What is the original number?

Question

11627 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-22T09:44:39

#35#

Let #x# & #y# be respectively unit & tenth digits of two-digit number then the number will be

#10y+x#

Condition 1: sum of digits is #8# hence

#x+y=8\ .........(1)#

Condition 2: When #18# is added to the number #10y+x# then digits are reversed i.e. number becomes #10x+y# hence

#18+10y+x=10x+y#

#9x-9y=18#

#x-y=2\ ..........(2)#

Adding (1) & (2) as follows

#x+y+x-y=8+2#

#2x=10#

#x=5#

Setting #x=5# in (1), we get

#5+y=8#

#y=3#

hence the number is

#10y+x#

#=10\cdot 3+5#

#=35#