Question

The ten digit of a two digit numbers is one more the ones digit .If the digits are interchanged the new numbers becomes 9 less than the original numbers.Find number

Answer 1

Answer:

98 , 87 , 76 , 65 , 54 , 43 , 32 , 21 , 10

Step-by-step explanation:

Let,

tens digit original number be a.

ones digit of the original number be b.

So, original number = $10a+b$

Now interchange to get the new number:

New number = $10b+a$

 It is given that , if the digits are interchanged the new numbers becomes 9 less than the original numbers.

So,   New number = Original numer - 9

$10b+a=10a+b-9$

Simplify the expression.

$10b+a=10a+b-9\\10b-b=10a-a-9\\9b=9a-9$

Divide both sides by 9.

$b=a-1$   -------------- (1)

Also given that, the ten digit of a two digit numbers is one more the ones digit.

$a=b+1$  

Rewrite by isolating $b$ to LHS.

$b=a-1$    --------------(2)

From (1) and (2), it is clear that (1) = (2).

Some of the numbers that satisfy the given conditions are,

98 , 87 , 76 , 65 , 54 , 43 , 32 , 21 , 10.