Question

A body weighs 160 g in air , 130 g in water and 130 g in liquid . What is the density of liquid?

Answer 1

Let the density of the body =  p kg/m³
                          its volume = v m³
weight of body in a medium = (density of body-density of medium)×v×g

Case:1
weight in air = 160g = 0.16kg × g m/s²   (g=acceleration due to gravity)
density of air ≈ 0
Thus
0.16×g = (p-0)vg
⇒v = 0.16/p

Case:2
weight in water = 130g = 0.13kg × g m/s²
density of water = w kg/m³
Thus 
0.13 × g = (p - w)vg
⇒p-w = 0.13/v
⇒p-w = 0.13/(0.16/p)
⇒p-w = 0.13p/0.16
⇒p-w = 13p/16
⇒p - 13p/16 -w = 0
⇒3p/16 = w
⇒p = 16w/3

Case:3
weight in oil = 136g = 0.136kg × g m/s²
density of oil = d kg/m³
Thus 
0.136 × g = (p - d)vg
⇒0.136 = (p-d)v
⇒0.136 = (p-d)(0.16/p)

⇒0.136 = (0.16)

⇒ 0.136/0.16 = 1-

⇒0.85 = 1 -

⇒0.85 = 1 - 

But accrding to defination of specific gravity, specific gravity of oil = 

⇒  = 1 - 0.85

⇒  = 0.15 

⇒ =  ×0.15

⇒ = 

⇒ = 0.8