A) 11
B) 9
C) 7
D) 6
Correct Answer: B
Solution :
Let the two digits number be \[10y+x.\] |
According to the question, |
\[10y+x=5(x+y)\] |
\[\Rightarrow \] \[10y+x-5x-5y=0\] ?(i) |
\[\Rightarrow \] \[5y-4x=0\] |
and |
\[10y+x+9=10x+y\] |
\[\Rightarrow \] \[9x-9y=9\] |
\[\Rightarrow \] \[x-y=1\] ?(ii) |
From Eq. (i), [from Eq. (ii)] |
\[\Rightarrow \] \[5y-4\,\,(1+y)=0\] |
\[\Rightarrow \] \[5y-4-4y=0\] |
\[\Rightarrow \] \[y=4\] |
\[\therefore \]From Eq. (ii), |
\[x=4+1=5\] |
\[\therefore \] Number\[=10\times 4+5=45\] |
\[\therefore \] Sum of digits\[=4+5=9\] |
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