Question

The product of digit of two digit no is 12 when 9 is added to the number the digit interchange their places. Determine the no

Answer 1

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Answer 2

Answer:

Number is 34.

Step-by-step explanation:

Given : The product of digit of two digit no is 12 when 9 is added to the number the digit interchange their places.

To find : Determine the number?

Solution :

Let the number be $10x+y$  .....(1)

The product of digit of two digit no is 12

$xy=12$

$\Rightarrow y=\frac{12}{x}$ .....(2)

When 9 is added to the number the digit interchange their places.

$10x+y+9=10y+x\\9x-9y=-9\\x-y=-1$ .....(3)

Substitute (2) in (3)

$x-\frac{12}{x}=-1$

$x^2-12=-x$

$x^2+x-12=0$

$(x+4)(x-3)=0$

$x=-4,3$

Reject x=-4

Then x=3

Substitute in (2),

$y=\frac{12}{x}$

$y=\frac{12}{3}$

$y=4$

Substitute x and y in (1)

$N=10(3)+4$

$N=30+4$

$N=34$

Therefore, Number is 34.