Question

The tens digit of a two-digit number is one more than the ones digit.If the digits are interchanged,the new number becomes 9 less than the original number.Find the number.​

Answer 1

Step-by-step explanation:

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

hope this helps you

Answer 2

Answer:

The numbers can be 10 , 21 , 32 , 43 , 54 , 65 , 76 , 87 , 98.

Step-by-step explanation:

Given :

• The tens digit of a two-digit number is one more than the ones digit.

• If the digits are interchanged, the new number becomes 9 less than the original number.

To find :

the number

Solution :

Let tens digit be x and units digit be y.

Then, the number is (10x + y)

If digits are interchanged, then

➙ units digit = x

➙ tens digit = y

the new number = (10y + x)

The new number becomes 9 less than the original number.

 10y + x = 10x + y - 9

 10y - y = 10x - x - 9

  9y = 9x - 9

  9y = 9(x - 1)

  y = x - 1

  x - y = 1 ➙ [1]

It's also given, the tens digit of a two-digit number is one more than the ones digit.

x = 1 + y ➙ [2]

equation [1] and equation [2] are same.

Hence, many two-digit numbers exist satisfying the given conditions.

Put y = 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8

then x = 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9

The numbers can be 10 , 21 , 32 , 43 , 54 , 65 , 76 , 87 , 98.