Question

One brother says of his younger brother: “Two years ago, I was three times as old as my brother was. In three years time, I will be twice as old as my brother.” How old are they each now?

Answer 1

Let B=age of big brother (older brother), L=age of little brother (younger brother).

Two years ago they were B-2 and L-2 years old.

B-2=3(L-2), B-2=3L-6, B=3L-4.

In three years' time their ages will be B+3 and L+3 years old.

B+3=2(L+3), B+3=2L+6, B=2L+3.

So (B=)3L-4=2L+3, L=7, making B=3L-4=2L+3=17.

The older brother is 17 and his younger brother is 7.