The relative density of a liquid is $0.5$ . The density bottle weighs $200 g$ when filled with water and $120 g$ when filled with the liquid. The mass of density bottle is:

$90 g$

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$50 g$

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$40 g$

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$60 g$

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Solution

The correct option is C
$40 g$

Let
Mass of empty density bottle = $m$
Mass of water filled in density bottle = $m_{w}$
Mass of the liquid filled in density bottle = $m_{l}$

Given:
$m$ + $m_{w}$ = $200 g$
$m$ + $m_{l}$ = $120 g$
Hence, $m_{w} - m_{l} = 80 g$ ...( $1$ )

Relative density of liquid = $0.5$

Density bottle carries equal volume of liquids. Hence, volume of water and the liquid is same.

Relative density of liquid =
$\frac{Density of liquid}{Density of water}$ = $\frac{m_{l}}{m_{w}}$ = $0.5$

Hence, $m_{l} = 0.5 m_{w}$ ....( $2$ )

By solving equation ( $1$ ) and ( $2$ ) $m_{w} = 160 g$
Given: $m$ + $m_{w}$ = $200 g$
$⟹ m = 200 g - 160 g = 40 g$

Hence, mass of density bottle = $40 g$

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The relative density of a liquid is 0.5. The density bottle weighs 200 g when filled with water and 120 g when filled with the liquid. The mass of density bottle is:

The relative density of a liquid is $0.5$ . The density bottle weighs $200 g$ when filled with water and $120 g$ when filled with the liquid. The mass of density bottle is: