Question

The difference of digits of a two digit
number is
3. on reverning of digits the
New number is Dimishing by 27 the original number find the Number​

Answer 1

Answer :

The two-digit number can be 30 , 41 , 52 , 63 , 74 , 85 , 96

Step-by-step explanation :

Given :

• The difference of digits of a two digit  number is  3.
• On reversing the order of digits , the new number is diminished by 27 than original number.

To find :

the number

Solution :

Let units digit be y and tens digit be x  

The, the number = 10x + y

The difference of digits of a two digit  number is  3

x - y = 3 ➙ [1]

(or) y - x = 3 (can be possible since it's not given which digit is greater)

On reversing the digit, the new number = 10y + x

the new number is diminished by 27 than original number.

10y + x = 10x + y - 27

10y - y = 10x - x - 27

 9y = 9x - 27

 9y = 9(x - 3)

  y = x - 3

  x - y = 3 ➙ [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

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

The two-digit number can be 30 , 41 , 52 , 63 , 74 , 85 , 96.