A) 72
B) 27
C) 54
D) 45
Correct Answer: B
Solution :
[b] Let the digits at units and tens place of the number be x and y respectively. |
\[\therefore \] The number is \[10y+x\] |
Number obtained by interchanging the digits \[=10x+y\] |
According to the question, |
\[x+y=9\] ...(1) |
and \[10x+y-(10y+x)=45\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,9x-9y=45\,\,\,\,\,\,\Rightarrow \,\,\,x-y=5\,\] ..(2) |
On adding eq. (1) and eq. (2). we get |
\[2x=14\Rightarrow x=7\] |
Substituting value of x in eq. (1), we get |
\[y=9-7=2\] |
Hence, the number is \[10(2)+7=27.\] |
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