An object is put one by one in three liquids having different densities. The object floats with `(1)/(9),(2)/(12) and (3)/(7)` parts of their volumes outside the liquid surface in liquids of densities `d_(1),d_(2) and d_(3)`, respectively. Which of the following statement is correct ?

Options

A. `d_(1)gtd_(2)gtd_(3)`
B. `d_(1)gtd_(2)ltd_(3)`
C. `d_(1)ltd_(2)gtd_(3)`
D. `d_(1)ltd_(2)ltd_(3)`

Answer

D

Explanation

In a liquid of higher density more part of the object remains outside the liquid. Since, the order of part of their volume outside the liquid is given by (part of the body out side the liquid) `prop` densities of liquid
`(1)/(9)lt(2)/(11)lt(3)/(7)`
Thus, the order of densities in increasing order is
`d_(1)ltd_(2)ltd_(3)`