The tens digit in a two-digit number
is greater than the unit's digit by 5.1f
the
digits are interchanged and the resulting
number is added to the original
number, the result is 99. What is the orginal
number?
Answers
There will be many steps,
If the tens digit is 5 more than the ones digit, then the ones digit can be 1, 2, 3 and 4. Now let's try them: -
If we take 1 as the ones digit, then it will be 61. If we interchange it, then it becomes 16. The original no. was 61, so 61 + 16 = 77. ❌
If we take 2 as the ones digit, then it will be 72. If we interchange it, then it becomes 27. The original no. was 72, so 72 + 27 = 99. ✅
So the final answer is 99!! :)
Step-by-step explanation:
Given :-
The tens digit in a two-digit number is greater than the unit's digit by 5.1f the digits are interchanged and the resulting number is added to the original number, the result is 99.
To find:-
What is the orginal number?
Solution:-
Let the units digit in a two-digit number be X
Then, the tens digit in the two-digit number
= greater than the units digit by 5
= Units digit + 5
= X+5
Then the number = 10(X+5)+X
= 10X+50+X
= 11X+50
The Original number = 11X+50
The number obtained by reversing the digits
= 10X+(X+5)
= 10X+X+5
= 11X+5
The New number = 11X+5
Given that
The sum of the numbers = 99
=> 11X+50+11X+5 = 99
=> (11X+11X)+(50+5) = 99
=> 22X+55 = 99
=> 22X = 99-55
=> 22X = 44
=> X = 44/22
=> X = 2
The units place number = 2
The tens place number = 2+5 = 7
The number = 72
Answer:-
The Original number for the given problem is 72
Check:-
The units digit = 2
The tens digit = 7
=> 5+2
=> Units digit + 5
and
The Original number = 72
The number obtained by reversing the digits = 27
Their sum = 72+27 = 99
Verified the given relations in the given problem.