Question

A two digits number is such that the product of the digits is 20. If 9 is subtracted from the number, the digits interchange their places. Find the number ​

Answer 1

Answer:#BAL

Hope this will help you........

Step-by-step explanation:

Answer 2

Answer :-

The number is 54.

Explanation :-

Let the digit and units place be 'x' and the digit at tens place be 'y'.

•°• Number = x + 10y

Since the product of the digits is 20,

•°• xy = 20 ....... (i)

When 9 is subtracted from the number, the digits interchange their places.

•°• Interchanged number = 10x + y

According to the question,

$= > 10x + y = x + 10y - 9 \\ = > 10x + y - x - 10y = - 9 \\ = > 9x - 9y = - 9 \\ = > 9(x - y) = - 9 \\ = > x - y = \frac{ - 9}{9} \\ = > x - y = - 1 \\ = > x = - 1 + y \: ........(ii)$

Putting the value of x in equation (i), we get

$= > ( - 1 + y)(y) = 20 \\ = > - y + {y}^{2} = 20 \\ = > {y}^{2} - y - 20 = 0 \\ = > {y}^{2} - 5y + 4y - 20 = 0 \\ = > y(y - 5) + 4(y - 5) \\ = > (y + 4)(y - 5) \\ = > y = - 4 \: or \: 5$

By neglecting -4, putting y = 5 in equation (ii), we get

$= > x = - 1 + y \\ = > x = - 1 + 5 \\ = > x = 4$

•°• Required number = x + 10y

= 4 + 10(5)

= 4 + 50

= 54

Hence, the required number is 54.