4. The sum of the digits of a two-digit number is 15. The number obtained by interchanging its
digits exceeds the given number by 9. Find the original number
5. The difference between a 2-digit number and the number obtained by interchanging
digits is 63. What is the difference between the digits of the number
Answers
Solution 4
Let the two digit number 10x + y.
"The sum of the digits of a two-digit number is 15"
On equating this we get,
➵ x + y = 15 __(i)
"The number obtained by interchanging its digits exceeds the given number by 9"
On equating this we get,
➵ 10y + x = 10x + y + 9
➵ 9y - 9x = 9
➵ - x + y = 1 __(ii)
By adding (i) and (ii) we get,
➵ y = 8
&
➵ x + 8 = 15
➵ x = 7
Number = 10x + y = 10(7) + 8
➵ 78
Answer : 78
______________________________
Solution 5
"The difference between a 2-digit number and the number obtained by interchanging
Orginal number = 10x + y
Orginal number = 10x + y
Interchanged number = 10y + x
➵ 10x + y - (10y + x) = 63
➵ 9x - 9y = 63
➵ 9(x - y) = 63
➵ x - y = 7
Hence difference between digits is 7.
Answer : 7
Question - 4
Given,
Sum of a digits of a two - digit number = 15
According to the problem,
x + y = 15 --------(1)
The number obtained by interchanging the digits exceeds the given number by 9
10y + x = 10x + y + 9
10y + x - 10x - y = 9
9y - 9x = 9
y - x = 1 ----(2)
Add (1) and (2)
x + y + y - x = 16
2y = 16
y = 16/2
y = 8
substitute y in eq - 1
x + y = 15
x + (8) = 15
x = 15 - 8
x = 7
substitute x and y in the number :
= 10x + y
= 10(7) + 8
= 78
Therefore, the original number is 78
Question - 5 :
let the number be 10x + y
When we interchange the number then the number becomes 10y + x
According to the problem,
10x + y - 10y + y = 63
9x - 9y = 63
9(x - y ) = 63
x - y = 63/9
x - y = 7
Therefore, the difference between the digits of the numbers is 7.