The apparent weight of a body in a liquid of density `d_(1)` is `m_(1)` and, in another liquid of density `d_(2)`, its apparent weight is `m_(2)`. What will be its apparent weight in a liquid of density `d_(3)`?

Explanation

Let the real weight of the body be M and its volume be V.
`therefore" "M-Vd_(1)=m_(1)" "...(1)`
and `M-Vd_(2)=m_(2)" "...(2)`
From equations (1) and (2), we get
`V=(m_(1)-m_(2))/(d_(2)-d_(1))`
Let the apparent weight of the body in the liquid of density `d_(3)` be `m_(3)`.
`therefore" "m_(3)=M-Vd_(3)=m_(1)+Vd_(1)-Vd_(3)`
= `m_(1)+V(d_(1)-d_(3))`
= `m_(1)+((m_(1)-m_(2))(d_(1)-d_(3)))/((d_(2)-d_(1)))`
= `(m_(1)(d_(2)-d_(1))+(m_(1)-m_(2))(d_(1)-d_(3)))/((d_(2)-d_(1)))`
= `(m_(1)(d_(2)-d_(3))-m_(2)(d_(1)-d_(3)))/((d_(2)-d_(1)))`