Question

Sum of a two digit number is 9 also nine times this number is twice the number obtaind by reversing the order of the digits

Answer 1

answer is The sum of the digits of a two -digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Answer 2

■GIVEN:-

•The sum of the digits of a two digit number is 9.And nine times this number is twice the number

obtained by reversing the order of digit .

$\:$

■TO FIND OUT:-Required number

$\:$

■SOLUTION:-

□Let the tens and unit digit be x and y respectively

□Then the number is

$\boxed{ \textsf{ = 10x + y}}$

□Then the number obtained by reversing its order

$\boxed{ \textsf{ = 10y + x}}$

□According to question

$\textsf{x + y = 9} ............(1)$

And

$\textsf{9(10x + y) = 2(10y + x)}$

$\rm \implies90x + 9y = 20y + 2x$

$\rm \implies88x - 11y = 0$

$\implies \rm8x - y = 0...........(2)$

On adding (1) and (2) ,we get

$\rm9x = 9 \implies \: x = 1$

Substituting this value of x in (2),we get

$\rm8 \times 1 - y = 0 \implies \: y = 8$

As we know the required number was 10x+y

Putting the value of x and y in above equation

$\rm10 \times 1 + 8 = 18$

$\boxed {\large{\therefore \rm \: required \: number \: is \: 18}}$