ronnie1985 wrote:Bobby and his younger brother Johnny have the same birthday. Johnny's age now is the same as Bobby's age was when Johnny was half as old as Bobby is now. What is Bobby's age now?
(1) Bobby is currently four times as old as he was when Johnny was born.
(2) Bobby was six years old when Johnny was born.

Please help convert the sentences in equations.

Let Johnny's present age be x and Bobby's present age be y.
Half of Bobby's age is y/2.
Johnny must have been y/2 years of age (x-y/2) years ago.
At that time Bobby must have been y - (x - y/2) = 3y/2 - x years of age.
So x = 3y/2 - x
2x = 3y/2
4x = 3y

(1) Bobby is currently four times as old as he was when Johnny was born.
When Johnny was born, Bobby must have been y - x years of age.
4*(y - x) = y
3y = 4x
This is just the same equation as what we get from the main question; NOT sufficient.

(2) Bobby was six years old when Johnny was born implies y - x = 6.
So we have 2 equations, 4x = 3y and y - x = 6.
x = 18 and y is 24.

So Bobby's age now is 24 years; SUFFICIENT.

The correct answer is B.