Question

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

Answer 1

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