For a rocket moving in free space, the fraction of mass to be disposed off to attain a speed equal to two times the exhaust speed is given by(e^2=7.4)

We know that, the equation which gives us the velocity of the rocket at any time t, when its mass is m, is as follows:

v = u log(m_o/m)

⇒ [m_o/(m_o- m_d)] = e^(v/u)

where m_d is the disposed mass while m_o is the initial mass in the rocket.

Now putting (v/u) = 2 as directed in the question we can get desired result for the fraction of mass to be disposed off(m_d/m_o) to attain a speed equal to two times the exhaust speed.