Answer :
Answer:
[tex]Original\ number = 74[/tex]
Step-by-step explanation:
Let x be the 10's digit and y be the units digit.
So the original number is [tex]10x + y[/tex] and its reversed number is [tex]10y + x[/tex]
Given:
From the given statement the sum of the two digit is 11.
[tex]x+y=11[/tex]
[tex]x=11-y[/tex] -------------------(1)
When the numbers reversed the new number is 27 less than the original number.
[tex](10x+y)-(10y+x)=27[/tex]
[tex]10x+y-10y-x=27[/tex]
[tex]9x-9y=27[/tex]---------------(2)
Now we substitute x value in equation 2 from equation 1.
[tex]9(11-y)-9y=27[/tex]
[tex]99-9y-9y=27[/tex]
[tex]99-18y=27[/tex]
Now we add +18y both side in above equation.
[tex]99-18y+18y=27+18y[/tex]
[tex]99=27+18y[/tex]
[tex]99-27=18y[/tex]
[tex]99-27=18y[/tex]
[tex]72=18y[/tex]
[tex]y=\frac{72}{18}[/tex]
[tex]y=4[/tex]
Now we substitute y = 4 in equation 1.
[tex]x=11-4[/tex]
[tex]x=7[/tex]
So the original number is [tex]10x+y = 10\times 7 + 4=70+4=74[/tex].
Therefore the original number is 74.