Question

the units digit of a two-digit number is twice the tens digit. If the digits are reversed, the new number is 9 less than the original number. What is the original number?

Answer 1

Answer:

36

Step-by-step explanation:

Here is the correct and complete question: The units digit of a two-digit number is twice the tens digit. If the digits are reversed, the new number is 9 less than twice the original number. What is the original number?

Lets assume the original number be"10y+x". (x is unit digit and y is 10th digit)

∴ if number is reversed then resulting number be "10x+y".

As given: x= 2y

        and $10x+y= 2(10y+x)-9$

Now, solving the equation to get original number.

$10x+y= 2(10y+x)-9$

Distributing 2 to 10y and x, then opening the parenthesis.

⇒ $10x+y= 20y+2x-9$

subtracting by (2x+y) on both side.

⇒ $8x= 19y-9$

subtituting the value of "x", which is equal to 2y.

∴ $8\times 2y= 19y-9$

⇒ $16y=19y-9$

subtracting both side by (16y-9)

⇒ $3y= 9$

cross multiplying

We get, $y= 3$

y=3

∵x= 2y

$x=2\times 3= 6$

∴ x= 6

Therefore, the original number will be 36 as x is the unit number and y as tenth number.