Question

3: When equal volumes of two metals are
mixed together, the specific gravity of alloy
is 4. When equal masses of the same two
metals are mixed together, the specific
gravity of the alloy now becomes 3. Find
specific gravity of each metal?​

Answer 1

Answer:

Let specific gravity be x and y respectively .

since

$spec.gravt. = \frac{density(object)}{densiy(water)}$

There density will be px and py . where p is density of water . Since p = 1 . So density is also x and y .

Now case 1 ,

Let equal volume is v .

So mass will be xv and yv

And mix them , new density will be

$= \frac{xv +yv }{v + v} = 4 \\ x + y = 8$

Similarly

Let equal mass be m.

volume = mass / density

So volume will be

m/x and m/y

New density

$= \frac{m + m}{ \frac{m}{x} + \frac{m}{y} } = 3$

$= \frac{xy}{x + y} = 3 \\ xy = 24$

From both equation

$x(8 - x) = 24 \\ {x}^{2} - 8x + 24 = 0 \\ x = \frac{8 \pm\sqrt{ - 32}} {2}$

I am getting imaginary values