1.

The sum of the digits of a two-digit numberys 9. Also mine times this number isAvice the number obtained by reversing the order of the digits. Find the number.Meena went to a bank to with​

Answer»

GIVEN :-

  • The sum of the digits of a two-digit number is 9
  • Nine times this number is  twice the number obtained by reversing the order of the digits

To Find :-

  • The number

Solution :-

Let the unit digit be x

And tens digits be y

\boxed {\rm {Number = 10y + x}}

\boxed {\textrm {Number formed after reversing the digits = 10x + y}}

According to the question,

\sf {x + y = 9 \dots (Eq. 1)}\\\\\\\sf {9 \ (10y + x) = 2 \ (10x + y)}\\\\\\\sf {88y - 11x = 0}\\\\\\\sf {-x + 8y =0 \dots (Eq. 2)}  

ADDING Eq. (1) and (2),

\boxed {\rm{9y = 9}}

\boxed {\rm {y = 1 \dots (Eq. 3)}}

PUTTING this value in Eq (1),

\underline {\boxed {\sf {x = 8}}}

Number = 10y + x

= 10 × 1 + 8

= 18


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