Solution:
Solution
As the body is floating the weight of boy must be equal to weight water displaced,
$$Vd= V_{1}d_{1}+V_{2}d_{2}$$ -------------(1)
and $$V_{1}+V_{2}=V$$ [given]
$$\Rightarrow V_{2}=(V-V_{1})$$ -------------(2)
Substituting (2) in (1),
$$\Rightarrow Vd= V_{1}d_{1}+Vd_{2}- V_{1}d$$
$$\Rightarrow V_{1}(d_{1}-d_{2})= Vd - Vd_{2}$$
$$\Rightarrow V_{1}=\dfrac{V(d-d_{2})}{d_{1}-d_{2}}=\left ( \dfrac{d-d_{2}}{d_{1}-d_{2}} \right )V$$
