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?

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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#