Question

the sum of the digits of a two digit number is 11. if the digits are reserved, the new number is 27 less than the original number. find the original number

Answer 1

74 is required answer

Answer 2

Let x = the 10's digit and y = the units digit:
:
just write what it says: 
"The sum of the digits of a two-digit number is 11."
x + y = 11
and
y = (11 - x); can use for substitution
:
"If the digits are reversed, the new number is 27 less than the original number. 
Original number: 10x + y
Reversed number: 10y + x
:
Then the equation would be:
(10y + x) = 10x + y - 27
10y - y + x - 10x = -27
9y - 9x = -27
Simplify, divide equation by 9
y - x = -3
:
Substitute (11-x) for y in the above equation
(11 - x) - x = -3
-2x = - 3 - 11
-2x = -14
x = -14/-2
x = +7 is the 10's digit
:
11 - 7 = 4 is the units digit
:
Checking solutions
74 - 47 = 27