Question

a number is such that the product of its digit is 12, when 36 is added in it ,the number get reversed, what is the number?​

Answer 1

Answer :-

The number is 26.

Solution :-

Let the digit at one's place be y and the digit at the ten's place be x.

The number is - 10x + y

Case - I :

Given the product of its digit is 12, i.e.

=> xy = 12

=> x = $\dfrac{12}{y}$     ....i.)

Case - II :

Given that when 36 is added in it, the number get reversed, i.e.

=> 10x + y + 36 = 10y + x

=> 10x - x + 36 = 10y - y

=> 9x + 36 = 9y

[Taking out 9 as common]

=> 9(x + 4) = 9(y)

9 gets cancelled and the remaining equation is this,

=> x + 4 = y

Substituting the value of x from the equation i.)

=> $\dfrac{12}{y}$  + 4 = y

=> $\dfrac{ 12 + 4y }{y}$ = y

=> 12 + 4y = y²

=> 0 = y² - 4y - 12

=> 0 = y² - (6 - 2)y - 12

=> 0 = y² - 6y + 2y - 12

=> 0 = y(y - 6) + 2(y - 6)

=> 0 = (y - 6)(y + 2)

=> y - 6 = 0 or y + 2= 0

=> y = 6 or y = -2

As, y cannot be negative.

Therefore, the value of y is 6.

Now, finding the value of x by substituting the value of y in equation i.)

=> x = $\dfrac{12}{y}$  

=> x = $\dfrac{12}{6}$

=> x = 2

The number is -

=> 10x + y

=> 10 × 2 + 6

=> 20 + 6

=> 26