In detail

The three brothers

The three brothers

Three brothers: Antonio, Benito and Carlos have different ages. Antonio is twice the age Benito will be when Carlos is twice the age Antonio is now.

Who is the older brother?

Solution

Carlos is the older brother and Benito the smallest.

Let's suppose:
A1, A2: Antonio's current and future age.
B1, B2: ages of Benito.
C1, C2: ages of Carlos.
And to pass from one age to another, X years must pass (X = B2-B1).

Mathematically, according to the statement:
A1 = 2 * B2
C2 = 2 * A1

Knowing that Benito is the smallest is easy:
A1 = 2 * B2> B2 = B1 + X> B1
C2 = 2 * A1 = 2 * 2 * B2> B2 = B1 + X> B1

Now to see who is the oldest:
C2 = C1 + X = C1 + B2-B1 = 2 * A1, then:
C1 = 2A1-B2 + B1 = A1 + A1-B2 + B1 = A1 + 2 * B2-B2 + B1 = A1 + B2 + B1> A1
since all amounts are positive.