The sum of the digits of a two digits number formed by reversing its digit is less than the original number by 9,find the original number
Answers
Correct Question:-
The sum of the digits of a two digit number is 9. If the number formed by reversing the digits is less than the original number by 9, Find the original number
Answer:-
Let the digit at units place be y and digit at ten's place be x.
The number = 10x + y
Given:
Sum of the digits = 9.
→ x + y = 9 -- equation (1)
And,
The number formed by reversing the digits is 9 less than the original number.
→ Number formed by reversing the digits = 10y + x.
According to the above condition,
→ 10x + y - 9 = 10y + x
→ 10x + y - 10y + x = 9
→ 9x - 9y = 9
→ 9(x - y) = 9
→ x - y = 9/9
→ x - y = 1 -- equation (2)
Add equations (1) & (2).
→ x + y + x - y = 9 + 1
→ 2x = 10
→ x = 10/2
→ x = 5
Substitute the value of x in equation (1).
→ x + y = 9
→ 5 + y = 9
→ y = 9 - 5
→ y = 4
The number = 10 * 5 + 4 = 50 + 4 = 54.
Therefore, the required number is 54.
Correct Question:
The sum of the digits of a two digits number is 9 and the number formed by reversing its digit is less than the original number by 9,find the original number
(Question is incomplete ^^" but in second half given that the number formed by reversing its digit is less than the original number by 9. So, we take a assumption that their sum is also 9).
Answer:
54
Step-by-step explanation:
Assume that the ten's digit be x and one's digit be y.
Therefore,
The original number is 10x + y and reversed number is 10y + x.
The sum of two digit number is 9.
→ x + y = 9
→ x = 9 - y
The sum of the digits of a two digits number formed by reversing its digit is less than the original number by 9.
As per given condition,
→ Original Number - 9 = Reversed Number
→ 10x + y - 9 = 10y + x
→ 10x - x + y - 10y = 9
→ 9x - 9y = 9
→ x - y = 1
Substitute value of x in above equation
→ 9 - y - y = 1
→ 2y = 8
→ y = 4
Substitute value of y in x
→ x = 9 - 4
→ x = 5
Hence, the original number is 54.