Question

The sum of the digits of a two-digit number is 9 the number obtained by interchanging its digits is 9 less than thrice the original number find the number

Answer 1

27 is the number

Step-by-step explanation:

let x,y are the digitaal the number be 10x+y

given that x+y=9 (eq.1)

number obtained by interchanging it's digit=10y+x=3(10x+y)-9

=10y+x= 30x+3y-9

=10y-3y= 30x-x-9

=7y= 29x-9

= 29x-7y=9(eq.2)

multiply 7 to eq.1=7(x+y=9)= 7x+7y=63 (eq.3)

add eq.2 and eq.3

29x-7y=9

7x+7y=63

________

36x+0=72

________

36x=72

x=72/36

x=2

substitute 'x' value in eq.1

2+y=9

y=9-2

y=7

Therefore the number 10x+y = 10(2)+ 7

=20+7=27

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