A 2 digit no is 4 times the sum of its digit .If 18 is added to number the digit are reversed.find the no
Answers
Given:
A two digit number is 4 times the Sum of its digits.
If 18 is added to the number the digits are reversed.
Find:
The original number
Solution:
Let the digit at unit's place be 'y' and the digit at ten's place be 'x'.
Number = 10x + y
A two digit number is 4 times the Sum of its digits
=> 10x + y = 4(x + y)
=> 10x + y = 4x + 4y
=> 10x - 4x = 4y - y
=> 6x = 3y
=> 2x = y ........(i).
If 18 is added to the number the digits are reversed
Number obtained by reversing the digits = 10y + x
Original number + 18 = Number obtained by reversing the digits
=> 10x + y + 18 = 10y + x
=> 10x - x + y - 10y = -18
=> 9x - 9y = -18
=> 9(x - y) = -18
=> x - y = -18/9
=> x - y = -2
Putting the value of 'y' from equation (i) in equation (ii).
=> x - y = -2
=> x - 2x = -2
=> x = -2
Putting the value of 'x' in equation (ii)
=> 2x = y
=> 2(-2) = y
=> -4 = y
=> y = -4
Now,
Number = 10x + y
=> 10(2) + 4
=> 20 + 4
Number = 24
Hence, the original number is 24.
I hope it will help you.
Regards.
Answer:
The answer of the number is 24, as 24 + 18 = 42.
I hope i got this correct, but if not, correct me if it's wrong :))
Have a good Sunday!!!