Question

The difference between a two-digit number and that number reversed is 18. What could that number be? List all possibilities.

Answer 1

Answer:

If the 2 digit no is 10x + y ,

the number with reverses digits will be 10y + x

The difference between them is 18. So,

10x +y -10y -x = 18. So

9x - 9y = 18. So

x-y= 2

Which means the set of two digit numbers whose difference in digits is 2 will be the solution.

These numbers are

13 , 31

24,42

35, 53

46, 64

57, 75

68, 86

79, 97

So such pairs are 7

Step-by-step explanation:

Answer 2

Answer:

The number is 64

Step-by-step explanation:

Let the tens digits be  "x" and unit digit be" y".

Let the number be 10x+y and

the reversed number is 10y+x.

According to the question, it is given that,

the difference between a two-digit number and that number reversed is 18.

Therefore,

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

10x+y-10y-x=18

9x-9y=18

9(x-y)=18

x-y=18/9

x-y=2.

Now, the possibilities of all the numbers are,

The number 64 is the possible answer as the reverse is 46 and according to the condition it is proven that

The difference between a two-digit number and that number reversed is 18.

so,

64-46=18

and also

6-4=2 , (x-y=2)

Hence, the number is 64.

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