the unit's digit of a two digit number is three more than the ten's digit.The number obtained by reversing the digits is 27 more than the original number.Find the original number.
Answers
Answer:
the two digit number can be any one of these number 30, 41, 52, 63, 74, 85, and 96
Step-by-step explanation:
Let the 10s digit of two digit number be x and 1s digit of two digit number be y.
Hence the number is 10x + y.
The ten digit of a two-digit number is 3 greater than the unit digit.
x = y + 3…Eq..1
When the digits are reversed, the number is reduced by 27.
On reversing the digits, the number will become 10y + x.
(10x + y) —27 = 10y + x
10x + y -10y - x = 27
9x - 9y = 27…Eq..2
Now substituting the value of x from Eq. 1 to Eq..2
9x - 9y = 27
9 (y + 3) - 9y = 27
9y + 27 - 9y = 27
9y - 9y = 27 - 27
0 = 0
This strange situation means the equation is true.
So we have to think the number in other way.
As per our assumption above y represents the 1s digit of a two digit number. So y should be an integer between 0 and 9 viz. 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9.
Each of these y values will provide corresponding x value using the Eq..1. So we have:
y = 0, x = 0 + 3 = 3
y = 1, x = 1 + 3 = 4
y = 2, x = 2 + 3 = 5
y = 3, x = 3 + 3 = 6
y = 4, x = 4 + 3 = 7
y = 5, x = 5 + 3 = 8
y = 6, x = 6 + 3 = 9
y = 7, x = 7 + 3 = 10
y = 8, x = 8 + 3 = 11
y = 9, x = 9 + 3 = 12
Since, x represents the tens digit of a two digit number. So x = 10, x = 11, and x = 12 cannot work, therefore these are to be omitted. So y = 7, y = 8, and y = 9 are rejected.
The rest of the y-values can provide us the possible two digit number. Let us see:
y = 0, x = 3 ---> Number is 30
y = 1, x = 4 ---> Number is 41
y = 2, x = 5 ---> Number is 52
y = 3, x = 6 ---> Number is 63
y = 4, x = 7 ---> Number is 74
y = 5, x = 8 ---> Number is 85
y = 6, x = 9 ---> Number is 96
So the possible numbers are 30, 41, 52, 63, 74, 85, and 96.
Let's check each of these two digit numbers to confirm the statement that, when the digits are reversed, the number is reduced by 27:
30 - 03 = 27
41 - 14 = 27
52 - 25 = 27
63 - 36 = 27
74 - 47 = 27
85 - 58 = 27
96 - 69 = 27
So, all seven of these numbers are providing numbers reduced by 27 on reversing. Hence the required two digit number can be any one of these number - 30, 41, 52, 63, 74, 85, and 96. All can be the solution of this problem.
Answer: the two digit number can be any one of these number 30, 41, 52, 63, 74, 85, and 96