Question

When two fluids of different densities having volume of $4\text{L}$ and $5\text{L},$ respectively are mixed, it results in a mass of $53\text{pounds}.$ When the same two liquids are mixed in the reversed proportion, the resulting mass is increased by $2\text{pounds}.$ Find the ratio of densities of the two liquids.

• A. $7:9$
• B. $7:5$

Answer 1

The correct option is B $7:5$

Let the density of the two liquids be $x\text{unit}$ and $y\text{unit},$ respectively.

We know, $\text{Volume}\times \text{Density}=\text{Mass}$

When the two liquids of $4\text{L}$ and $5\text{L}$ are mixed, the resulting mass is $53\text{pounds}.$
$\Rightarrow 4x+5y=53...\left(a\right)$
Here the ratio of mixing is $\frac{4x}{5y}=4:5$
The reversed ratio of mixing is $5:4.$
$\therefore$ Equation of the second solution is
$5x+4y=53+2=55...\left(b\right)$

Let's eliminate $x$ by multiplying constants with the equaions, and subtrating them.
$5\times \left(a\right)-4\times \left(b\right)$
$\Rightarrow 5(4x+5y)-4(5x+4y)=5\left(53\right)-4\left(55\right)$
$\Rightarrow 25y-16y=45$
$\Rightarrow y=\frac{45}{9}=5\text{unit}$

Substitute $y$ in (a).
$4x+5\left(5\right)=53$
$\Rightarrow x=\frac{53-25}{4}=7\text{unit}$

$\therefore$ The ratio of the densities is $\frac{x}{y}=\frac{7}{5}=7:5$