Maths
posted by joshua on .
The sum of the 2digits of a 2 digit number is 15. If th number formed by reversing the digits is less than the orginal number by 27.Find the orginal number

Let the number be ab
a+b=15
10b+a = 10a+b  27
a + b = 15
9a + 9b = 27
a + b = 15
a  b = 3
2a = 18
a=9
b=6
check: 69 = 96  27 
Answering by logic and mental calculations:
Since the order of digits is not important (they will be reversed anyway), the only twodigit combinations that add up to 15 are (8,7) and (6,9).
(8,7) does not work because 8778=9. Now try 9669=27, which is obviously the answer. 
When we have a two digit number, it can be expressed as :
10 a + b
In this case :
10 a + b = orginal number
The sum of the 2 digits is 15
a + b = 15 Subtract a to both sides
a  a + b = 15  a
b = 15  a
If you reverse the digits of 10 a + b, it will be :
10 b + a
10 b + a = orginal number  27 Add 27 to both sides
10 b + a + 27 = orginal number  27 + 27
10 b + a + 27 = orginal number
10( 15  a ) + a + 27 = orginal number
150  10 a + a + 27 = orginal number
177  9 a = orginal number
Also
10 a + b = orginal number
10 a + 15  a = orginal number
9 a + 15 = orginal number
177  9 a = 9 a + 15 Subtract 15 to both sides
177  9 a  15 = 9 a + 15  15
162  9 a = 9 a Add 9 a to both sides
162  9 a + 9 a = 9 a + 9 a
162 = 18 a Divide both sides by 18
162 / 18 = a
9 = a
a = 9
b = 15  a
b = 15  9 = 6
orginal number = 10 a + b = 10 * 9 + 6 = 90 + 6 = 96