| If the positions of the digits of a two-digit number are interchanged, the number obtained is smaller than the original number by 27. If the digits of the number are in us ratio of 1: 2, then what is the original number? |
A) 36
B) 48
C) 63
D) 56
E) None of these
Correct Answer: C
Solution :
| Let the digits at one place be x and ten's place be y. |
| Then, according to the question, |
| \[\frac{x}{y}=\frac{1}{2}\]\[\Rightarrow \]\[2x-y\] (i) |
| and \[10x+y=(10y+x)=-\,\,27\] |
| \[\Rightarrow \] \[9x-9y=-\,\,27\] |
| \[\Rightarrow \] \[9y-9x=27\] |
| \[\Rightarrow \] \[y-x=3\] |
| On solving Eqs. (i) and (ii), we get |
| \[2x-x=3\] |
| \[x=3\] and \[y=6\] |
| \[\therefore \] Number is 63. |
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