SSC Sample Paper Mock Test-20 SSC CGL Tear-II Paper-1

A two digit number is five times the sum of its digits. If 9 is added to the number, the digits interchange their positions. The sum of digits of the number is

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\[=4+5=9\]