Question

The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18.then the number is:
2 points

Answer 1

Answer:

our number ( xy) is 53, as x= 5 and y=3.

Step-by-step explanation:

Firstly we have to create a basic idea about the question. A number, suppose 89 can be written in expanded form as ((8x10)+ (9x1)). This idea will help us solve the problem.

Note - (xy)and (yx) represent the number, not the product of x and y.

Let the number be (xy), in expanded form it can be written as (10x + y). It is given that sum of the digits,that is x and y, is 8. Therefore we can state, x+y = 8.

When we reverse (xy) it becomes (yx), in expanded form it can be written as (10y + x). Again it is given that difference between the two numbers is 18. Therefore we can say, (xy) - (yx)= 18.

Now , (xy) - (yx) = 18, which implies ( 10x +y)- (10y+x) = 18.

Simplifying further,

( 10x - x - 10y + y) = 18

9x - 9y =18

9(x-y)= 18 ( Taking common factor 9)

x-y= 18/9 (Transposing 9 to RHS)

x-y=2.

Earlier we stated that, (x +y) = 8. Now we can combine, (x-y)= 2 and ( x+y)= 8.

(x+y)+(x-y) = 8+2

2x = 10

x= 5 ( Transposing 2 to RHS).

Now, x= 5 and (x+y)= 8, we can state y= 3.

So, our number ( xy) is 53, as x= 5 and y=3.

We can check the answer by subtracting 35 from 53, which is 18.

hope it helped:)