a number consists of two digit when the number is divided by the sum of its digit the quotient is 7 if 27 is subtracted from the no the digit interchange their places find the numbers
Answers
Given:
A number consists of two digits when the number is divided by the sum of digit the quotient is 7.
If 27 is subtracted from the numbers, the digits interchange their places.
Find:
the number
Solution:
Let the digit at unit's place be 'y' and the digit at ten's place be 'x'
Then,
Number = 10x + y
A number consists of two digits when the number is divided by the sum of digit the quotient is 7
=> (10x + y)/(x + y) = 7
Use cross multiplication
=> 10x + y = 7(x + y)
=> 10x + y = 7x + 7y
=> 10x - 7x = 7y - y
=> 3x = 6y
=> x = 2y ......(i).
If 27 is subtracted from the numbers, the digits interchange their places.
Number obtained by reversing the digits = 10y + x
Original number - 27 = Number obtained by reversing the digits
=> 10x + y + 27 = 10y + x
=> 10x - x + y - 10y = -27
=> 9x - 9y = -27
=> 9(x - y) = -27
=> x - y = -27/9
=> x - y = -3 ......(ii).
Putting the value of 'x' from equation (i) in equation (ii)
=> x - y = -3
=> 2y - y = -3
=> y = -3
Now, put the value of 'y' in equation (i)
=> x = 2y
=> x = 2(-3)
=> x = -6
Now,
Number = 10x + y
=> 10(6) + 3
=> 60 + 3
=> 63
Hence, the number is 63.
I hope it will help you.
Regards.
Answer:
Putting the value of 'x' from equation (i) in equation (ii)
=> x - y = -3
=> 2y - y = -3
=> y = -3
Now, put the value of 'y' in equation (i)
=> x = 2y
=> x = 2(-3)
=> x = -6
Step-by-step explanation: