Question

The sum of the digits of a two-digit number is 3.if we subtract 9 from the number,the Digits are interchanged.find the original number.

Answer 1

Let Tens Place Digit be=X

Let Ones Place Digit be=Y

Sum of Digit=3

x+y=3 (Equation 1)

Original Number=10x+y

(Why we Multiply 10 in number.How the number 99 is made.By 9+9 no.By 10×9+9=99.

hOpe you Understand)

Original Number=10x+y

Reverse Number=10y+x

When we subtract 9 from original number number become Reverse.

A/Q

10x+y-9=10y+x

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

10x+y-10y-x=9

9x-9y=9

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

x-y=9/9

x-y=1

We got

X+Y=3

X=3-Y

X-Y=1

3-y-y=1. (x=3-y)

3-2y=1

3-1=2y

2=2y

y=2/2

y=1

We get Y=1

We know

x-y=1

x-1=1

x=1+1

x=2

X=2

Y=1

Number=10x+y

=10×2+1

=21

Number=21

Check.

Subtract 9=Reverse

21-9=12

Hence it is right

$\boxed{\boxed{\mathbf{Original\:Number=21}}}$