A) 11
B) 9
C) 7
D) 5
Correct Answer: B
Solution :
Let the two digit number be \[=10x+y\] |
According to the question, |
\[10x+y=3\,\,(x+y)\] |
\[\Rightarrow \]\[10x+y=3x+3y\] |
\[\Rightarrow \] \[10x+y-3x-3y=0\] |
\[\Rightarrow \] \[7x-2y=0\] |
and \[10x+y+45=10y+x\] ?(i) |
\[\Rightarrow \] \[10y+x-10x-y=45\] |
\[\Rightarrow \] \[9y-9x=45\] |
\[\Rightarrow \] \[9\,\,(y-x)=45\] |
\[\Rightarrow \] \[y-x=5\] |
\[\Rightarrow \]By \[2\times \]Eq. (ii) + Eq. (i), we have ?(ii) |
\[2y-2x+7x-2y=10\] |
\[\Rightarrow \] \[5x=10\] |
\[\Rightarrow \] \[x=\frac{10}{5}=2\] |
From Eq. (ii), |
\[y-2=5\]\[\Rightarrow \]\[y=2+5=7\] |
\[\therefore \] Number \[=10x+y=2\times 10+7=27\] |
\[\therefore \] Sum of digits \[=2+7=9\] |
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