Question

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

Answer 1

Answer:

The number is 54

Step-by-step explanation:

Let the Numbers be “x” and “y”

For Number of two digits

We use

10x+y

According to question

10x + y = 6 (x + y) ………1(equation 1)

And

10x + y - 9 = 10y + x ……2(equation 2) { Reversed }

Now

From Equation 2

10x - x + y -10y - 9 = 0

9x - 9y -9 =0

Taking 9 Common

9 (x - y - 1)= 0

x - y- 1 =0

so x =y + 1 …….3(equation 3)

Now Put the Value of “x” in equation 1

It becomes

10(y+1)+y=6((y+1)+y)

10(y+1)+y=6(y+1+y)

10y + 10 +y=6(2y+1)

11y + 10= 12y + 6

10-6=12y-11y  

4=y

So the Value of y is 4

Now Put the Value of “y” in equation 3

we get

x=y+1

=4+1

=5  

So the Two number is

10x + y

= 10×5 + 4

=54

So the number is 54

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and sorry for being that long