Question

A number of two digits is six times the sum of its digits. If 9 is subtracted from the number,
the digits are reversed. What is the number?

Full solution needed written in copy written plzzz ​

Answer 1

Solution :-

Let :-

Digit in ten's place = x

Digit in one's place = y

Two digit number = 10x +  y

According to the first condition :-

$\longrightarrow \sf 10x+y = 6(x+y) \\\\\longrightarrow 10x+y= 6x+6y \\\\\longrightarrow 10x-6x+y-6y = 0 \\\\\longrightarrow 4x-5y = 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .............(1)$

According to the second condition :-

$\longrightarrow \sf 10x+y - 9 = 10 y + x \\\\\longrightarrow 10x-x+y-10y = 9 \\\\\longrightarrow 9x-9y = 9 \\\\\longrightarrow x-y = 1 \\\\\longrightarrow x = y+1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .............(2)$

Substitute the value of x in eq (1) :-

$\longrightarrow \sf 4(y+1) - 5y = 0 \\\\\longrightarrow 4y+4 -5y = 0 \\\\\longrightarrow -y = - 4 \\\\\longrightarrow \bf y = 4$

Substitute y = 4 in eq (2) :-

$\longrightarrow \sf x = 4+1 \\\\\longrightarrow \bf x = 5$

Two digit number = 54

Answer 2

Answer:

See the answer down or in pinned .

Step-by-step explanation:

Let the one digit be x and another be y

Let the two digits be 10x +4

According to the question,

In first case:

10x+y = 6(xty)

or, 10x+y = 6x+6y

or, 10x - 6x + y - 6y = 0

or, 4x - 5y = 0 .........(1.)

In second case :

10x+y - 9 = 10 y+x

or, 10 x - x + y - 10 y = 9

or, 9x - 9y = 9

or, 9(x - y) = 9

or, x-y = 1

or, x = y + 1 ........(2.)

solving | Substituting the value of x in eq. (i) , we get ,

4x-5y = 0

or, 4(y+1) - 5y = 0

or, 4y + 4 - 5y = 0

or, -y = -4

or, y = 4

putting the value of y in eq. (2.)

x = y+1

or, x = 4+1

or, x = 5

Hence, the two digit be 10x + y

=10×5 + 4 = 54