Question

the sum of the digits of a two digit number is 9 if 9 is added to the number the digits are reversed find the number​

Answer 1

Answer is in attachment

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Answer 2

Let Ones Place Digit=x

Let Tens Place Digit=y

Sum of Digits=9

x+y=9

x=9-y. (Equation 1)

Number=10y+x

Why Number=10y+x

Take Number 69 how this Formed.

6+9=15 no. How? 6×10+9=69

That's Why we Multiply 10.

So original Number=10y+x

Reverse Number=10x+y

When 9 added to Original Number=Reverse Number.

10y+x+9=10x+y

9=10x+y-(10y+x)

10x+y-10y-x=9

9x-9y=9

9(x-y)=9. (common=9)

x-y=9/9

x-y=1

We know x=9-y

MEANS

x-y=1

9-y-y=1

-2y=1-9

-2y=-8. (- -=+)

y=8/2

y=4

We got y=4

And We know.

x-y=1

x-4=1

x=1+4

x=5

Number=10y+x

10×4+5

=45

$\boxed{\mathbf{Original\:Number=45}}$