Age Problems

Typically, in these problems, we start by letting x be a person's current age and then the person's age a years ago will be x Â–â€“ a and the person's age a years in future will be x + a. An example will illustrate.

Example:

John is 20 years older than Steve. In 10 years, Steve's age will be half that of John's. What is Steve's age?

(A) 2

(B) 8

(C) 10

(D) 20

(E) 25

Steve's age is the most unknown quantity. So we let x = Steve's age and then x + 20 is John's age. Ten years from now, Steve and John's ages will be x + 10 and x + 30, respectively.

Summarizing this information in a table yields

 Age now Age in 10 years Steve x x + 10 John x + 20 x + 30

Since "in 10 years, Steve's age will be half that of John's," we get

$\frac{1}{2}$ ( x + 30) = x + 10

x + 30 = 2(x + 10)

x + 30 = 2x + 20

x = 10

Hence, Steve is 10 years old, and the answer is (C).