Question

An adulterated sample of milk has a density $1032kg{m}^{-3}$ ,while pure milk has a density of $1080kg{m}^{-3}$. Then the volume of pure milk in a sample of $10$ litres of adulterated milk is

• A. $1$ litre
• B. $2$ litre
• C. $3$ litre
• D. $4$ litre

Answer 1

Answer: (D)

Mass of adulterated milk
$M_A=1032\times (10\times 10^{-3})kg$
or $M_A=10.32kg$ $(\because 1litre=10^{-3}{m}^3)$
Mass of pure milk $M_p=1080\times V_p$
$\therefore$ Mass of water added $={\rho }_w{V}_w=M_A-M_p$
$\therefore 10^3\times$ (volume of water added) $=M_A-M_p$
$\therefore 10^3\times \left(10\times 10^{-3}-V_p\right)=10.32-1080V_p$
or $80V_p=0.32$
or $V_p=\frac{0.32}{80}=\frac{1}{250}{m}^3=\frac{1000}{250}$
litre = $4$ litre.