Sum of the digits of a two-digit number
is 5. When we interchange the digits, it is
found that the resulting new number is
less than the original number by 27.
What is the two-digit number?
Answers
Given:
Sum of the digit of a two digit number is 5.
When we interchange the digit it is found that the resulting new number is less than the original number by 27.
Find:
The two digit number.
Solution:
Let the digits at ten's place be x.
Let the digits at unit's place by y.
Number => 10x + y
Sum of the digit of a two digit number is 5.
=> x + y = 5
=> x + 5 - y ..........(i).
When we interchange the digit it is found that the resulting new number is less than the original number by 27.
Reversed number = 10y + x
Reversed number = original number - 26
=> 10y + x = 10x + y - 27
=> 27 = 10x + y - 10y - x
=> 27 = 9x - 9y
=> 27 = 9(x - y)
=> 27/9 = x - y
=> 3 = x - y ...........(ii).
Putting the value of x from Eq (i). in Eq (ii).
=> 3 = x - y
=> 3 = 5 - y - y
=> 3 = 5 -2y
=> 3 - 5 = -2y
=> -2 = -2y
=> y = -2/-2
=> y = 1
Putting the value of y in Eq (i).
=> x + 1 = 5
=> x = 5 - 1
=> x = 4
So, Number => 10x + y
=> 10(4) + 1
=> 40 + 1
=> 41
Hence, the number formed is 4.
I hope it will help you.
Regards.
Answer:
=> 3 = x - y ...........(ii).
Putting the value of x from Eq (i). in Eq (ii).
=> 3 = x - y
=> 3 = 5 - y - y
=> 3 = 5 -2y
=> 3 - 5 = -2y
=> -2 = -2y
=> y = -2/-2
=> y = 1
Putting the value of y in Eq (i).
=> x + 1 = 5
=> x = 5 - 1
=> x = 4
Step-by-step explanation: