Since , external force on system is zero , so no change takes place in the centre of mass .

`x_(cm) = (m_1x_1 + m_2 x_2)/(m_1 + m_2)`

or ` Delta x_(cm) = (m_1 Delta x_1 + m_2 Delta x_2)/(m_1 + m_2)`

Here       `Delta x_(cm) = 0`

`:.`          `m_1 Delta x_1 + m_2 Delta x_2 = 0`

or            ` M Delta x_1 + M/3 Delta x_2 = 0`

`:.`         `    Delta x_1 = - (M)/(3M) Delta x_2 =  - (Delta x_2)/(3)`........................(i)

But             `x_(rel) = Delta x_1 - Delta x_2`

or            `L= Delta x_1 - Delta x_2`

or             ` L = - (Delta x_2)/(3) - Delta x_2 =  - 4/3 Delta x_2`           [from eq.(i)

`because   Delta x_2 = - 3/4 L`

`:.`            `Delta x_1 = - (Delta x_2)/(3)   = - (-3L)/(4 xx 3) = - L/4`

Negative sign indicates that both moves in opposite directions.