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
Answers
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.
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.