SSC Sample Paper Mock Test-11 SSC CGL Tear-II Paper-1

A 2-digit number is 3 times the sum of its digits. If 45 is added to the number, its digits are interchanged. The sum digits of the number is

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 \[=2+7=9\]