1.

a number consists of two digits whose sum is 9.if 27 is subtracted from the number its digits are reversed find the number

Answer»

Part 1
Initial number
let x be the digit in UNIT place
therefore the digit in ten's place = 9 - x (* 10)= 90 - 10x

Part 2
final number the digits are REVERSED,
in unit place = 9 - x
in ten's place = x (* 10)= 10x

Given,
90-10x + x(sum of digits)=9
90 -9x = 9
90 - 9x - 27=10 + 9 - x
90 - 9x - 27=9x + 9
(transpose)
90 - 27 - 9 = 9x + 9x
54= 18x
54/18 = x
3= x

Part 1
initial number unit's place= x=3
ten's place = 9 - x
9-3=6
there fore 63

check:
63-27=36.


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