Question

The difference between Alan's and Bea's age is three years. The sum of their ages is twenty-seven years. How old are they if-

A. Alan is older than bea?
B. Bea is older than Alan?

Answer 1

a - b = 3
a + b = 27
--------------add
2a = 30
a = 30/2
a = 15 <=== alan is 15

a + b = 27
15 + b = 27
b = 27 - 15
b = 12 <=== bea is 12

Answer 2

Alright. Take x as Alan's age, and y as Bea's age. We can start writing equations; from the first sentence, we find that x - y = 3. From the second sentence, x + y = 27. Adding the two equations, gives 2x = 30. Thus, x is 15, and it follows, that y = 15 - 3, or 12. So for A, Alan is 15, and Bea is 12, and for B, Bea is 15, and Alan is 12.