Question

a liquid mixture of volume V has two liquids as its ingredients with densities alpha and beta .if density of the mixture is ∆ then mass of the first liquid in mixture is

Answer 1

A liquid mixture of volume V has two liquids as its ingredients with densities α and β. If density of the mixture is ∆ then mass of the first liquid in mixture is

$\boxed{\frac{V\alpha(\beta-\Delta)}{\beta-\alpha}}$

Explanation:

We know that

Density = Mass / Volume

Let the mass of the liquids with densities $\alpha$ and $\beta$ be $M_1$ and $M_2$ respectively.

Then total mass

$M=M_1+M_2$

But

$M=V\times \Delta$

Therefore,

$V\times\Delta=M_1+M_2$   ......... (1)

Also total Volume

$V=V_1+V_2$

$\implies V=\frac{M_1}{\alpha}+\frac{M_2}{\beta}$

$\implies V=\frac{M_1}{\alpha}+\frac{V\times\Delta-M_1}{\beta}$

$\implies V=\frac{M_1\beta+V\Delta\alpha-M_1\alpha}{\alpha\beta}$

$\implies V\alpha\beta=V\Delta\alpha+M_1(\beta-\alpha)$

$\implies V\alpha (\beta-\Delta)=M_1(\beta-\alpha)$

$\implies M_1=\frac{V\alpha(\beta-\Delta)}{\beta-\alpha}$

Hope this answer is helpful.

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