Question

in a number of two digits units digit twice the tens digit if 36 to be added to the number the digits are reversed find the number

Answer 1

Answer:

If 36 be added to the number, the digits are reversed and the unit’s digit is 2 times the ten’s digit, then the number is option (c): 48.

Step-by-step explanation:

Let the unit’s digit be “y” and the ten’s digit be “x”, so, the number will be “(10x + y)”.

Case 1:

It is given that the unit’s digit is twice the ten’s digit, therefore, we get

y = 2x ……. (i)

Case 2:

Also given that, when 36 is added to the number (10x + y), then the digits are reversed to “(10y + x)”, therefore, we get

[10x + y] + 36 = 10y + x

⇒ 9x – 9y + 36 = 0

Substituting y = 2x from eq. (i)

⇒ 9x – (9*2x) = - 36

⇒ 9x – 18x = - 36

⇒ - 9x = -36

⇒ x = 4

∴ y = 2x = 2*4 = 8

Thus,

The number is = (10*4) + 8 = 40 + 8 = 48

Answer 2

Given: In a number of two digits units digit twice the tens digit if 36 to be added to the number the digits are reversed.

To find: The number.

Solution:

Let the digit in the tens place be x and the digit in the units place be y. So the number can be written as (10x+y). According to the question, the units digit is twice the tens digit. This can be represented as follows.

$y = 2x$

If 36 is added to the number, then the digits of the numbers are reversed. An equation can be formed as follows.

$10x + y + 36 = 10y + x$

$9x - 9y + 36 = 0$

On substituting y as 2x,

$9x - 18x + 36 = 0$

$9x = 36$

$x=4$

$y = 2(4)$

  $= 8$

Hence, the number can be written as follows.

$10x + y = 10(4) + 8$

            $= 48$

Therefore, the number is 48.