An object of mass $m_1$  collides elastically with another object of mass $m_2$ , which is at rest. After the collision the objects move with equal speeds in opposite directions. The ratio of the masses  $m_2:m_1$  is

Before collision,  $u_1=u;u_2=0$,                   A her collision  $v_1=-v;v_2=v$
If the collision is elastic, then we can write $u_1-u_2=v_2-v_1\Rightarrow u=2v$ ___(1)
Applying principle of conservation of momentum  $m_{1}u=(m_2-m_1)v\_\_\_\_\left(2\right)$
From (1) & (2) we get  $\frac{m_2}{m_1}=3$