The sum of the digits of a two-digit number is 7. When the digit are reversed,the numbers is increase by 27. How do you find the numbers?

2 Answers
Alan P.
May 16, 2018

The digits are #2# and #5#

Explanation:

If we let the digits be #color(blue)a# and #color(blue)b#
then the possible numbers composed of those two digits are
#color(blue)(10a+b)# and #color(blue)(10b+a)#

We are told
[1]#color(white)("XXX")color(blue)a+color(blue)b=7#
and (assuming #10a+b# is the larger composite number)
[2]#color(white)("XXX")(color(blue)(10a+b))-(color(blue)(10b+a))=27#

[2] simplifies into
[3]#color(white)("XXX")9a-9b=27#
or
[4]#color(white)("XXX")a-b=3#

Adding [1] and [4], we get
[5]#color(white)("XXX")2a=10#
which implies
[6]#color(white)("XXX")color(blue)a=5#

Substituting #5# for #color(blue)a# back in [1]
we see that
[7]#color(white)("XXX")color(blue)b=2#

Binayaka C.
May 16, 2018

The two digit number is #25#

Explanation:

Let tens digit and units digit of the number be

#x and y ; x+y=7; (1)#

The two digit number is #10 x+y#, when reversed,

the two digit number becomes #10 y+x#, by given condition,

#10 y+x =10 x+y+27 or 9 y -9 x =27 # or

# 9 (y - x) =27 or (y-x)=3 or y = x+3 # Putting

#y=x+3# in equation (1) we get, # x+x +3=7; # or

#2 x= 4 :. x =2 ; y= 2+3=5 #

Hence the two digit number is #25# [Ans]

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