Question

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

Answer 1

Step-by-step explanation:

let the number be xy

Then x-y = 3

Now the original number = 10x + y

on reverse the number becomes yx

the number = 10y + x

As per Equation

new number will get diminished (reduced)

therefore by equating original number and new number

10x + y = 10y + x + 27

We get 10x - x + y - 10y = 27

9x - 9y = 27

as 9 is common in all divide it by 9

x- y = 3

That means you will have variable

Numbers are:

30

41

52

63

74

85

96

you will get seven variable numbers.

Answer 2

Given

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

To find :

The number.

Solution :

Let two-digit numbers are x and y

Units digit is y

Tens digit = 10x

So, The number is 10x + y

Reversing the digits = 10y-x

Difference = 3

The new number diminished by 27

According to the given question

=> 10x + y - 10y - x = -27

=> 9x - 9y = -27

=> 9(x - y) = -27

=> x - y = -3

=> So, x - y = -3

Reversing y - x = 3.

Ten digit number should be more than the units digit. so , we can choose y = 9 and x = 6 that equals to 96.

The difference between these two numbers is 3.

=> 9 - 6 = 3.

On, Reversing the digits, The new number diminished by 27 than the original number.

=> Reverse of 96 = 69

=> 96 - 69 = 27.

There would be other numbers as answers for this question such as 85, 74, 63, 52, 41.

Hence: The Number Can be 96, 85, 74, 63, 52, 41.