sum of the digits of two digit number is 11. when we interchange the digits it is found that the resulting number is less than the original number by 9. what is the two digit number?
Answers
Answer :
The number is 65
Step-by-step Explanation :
Given : 1) Sum of the digits of two digit number is 11.
2) when we interchange the digits it is found that the
resulting number is less than the original number by 9.
To find : what is the two digit number = ?
let, the number is xy
According to the given conditions , x + y = 11 --------- (1)
After Interchanging , the number is yx
now,
[(10 × x) + y] - [(10 × y)+x] = 9
9x - 9y = 9
x - y = 1 ----------- (2)
After adding equation (1) & (2) we get,
2x = 12
= x = 6
Substituting the x = 6 in equation (1) we get ,
y = 5
hence, the number is 65
Step-by-step explanation:
Solution :
Let,
- Units digit = x
- Tens digit = 11 -x
Original number =
10 (11 -x) + x
110 - 10x + x
110 - 9x
When we interchange the digits =
10 (x) + (11 -x)
10x + 11 - x
9x + 11
★ According to the Question :
When we interchange the digits it is found that the resulting number is less than the original number by 9.
⇒ 110 - 9x - 9 = 9x + 11
⇒ 110 - 9 - 9x = 9x + 11
⇒ 101 - 9x = 9x + 11
⇒ 101 - 11 = 9x + 9x
⇒ 90 = 18x
⇒ x = 90/18
⇒ x = 5
Units digit = 5
• Tens digit = 11 -x
11 - 5 = 6
Number = 65
Therefore, the two digit number is 65.