Question

German silver is a mixture of copper, nickel and zinc. $\dfrac{3}{4}$ of the total mass is copper and $\dfrac{3}{8}$ of the remainder is nickel. What mass of German silver will contain $8\dfrac{1}{2}$ kg of zinc?
$a.{\text{ }}45\dfrac{2}{5}kg$
$b.{\text{ 50}}\dfrac{1}{5}kg$
$c.{\text{ 68}}kg$
$d.{\text{ }}54\dfrac{2}{5}kg$

Answer 1

Hint : We are supposed to make some assumptions and find out the correct way to divide the remainders, such that each element's proportions are identified correctly. We will have to bring out a comparison equation, from the data given in question. We can give certain variables unknown values.

Complete Step By Step Answer:
Let us assume that we have ‘x’ number of German Silver.
This German Silver comprises Copper, Nickel and Zinc.
It is given that copper mass is around $\dfrac{3}{4}$ of the total mass. Hence, we can write It as $\dfrac{3}{4}$ x.
Further, the remaining mass will be, $1x - \dfrac{{3x}}{4} = \dfrac{{1x}}{4}$ , $1x$ being the total mass.
Now amongst the remaining, the around $\dfrac{3}{8}$ of the remainder is nickel. That means, the remaining, $\dfrac{5}{8}of\dfrac{{1x}}{4}$ is zinc mass. $(i)$
In Question it is given that zinc is about $8\dfrac{1}{2}$ kg, which is = $\dfrac{{17}}{2}$ kg $(ii)$
Comparing the $(i){\text{ and }}(ii)$ equation, we get:
$\dfrac{5}{8}of\dfrac{{1x}}{4} = \dfrac{{17}}{2}$
$\dfrac{5}{8} \times \dfrac{{1x}}{4} = \dfrac{{17}}{2}$
$x = 54\dfrac{1}{2}$
So, the mass of German silver is: $x = 54\dfrac{1}{2}$ kg.
Option D is correct.

Note :
We will have to make sure that the given data is translated in such a form that it is easier to find out the solution. Also, remember to stick to the units which are given in the question. Rearrangement of units can be done to interpret which will lead one to their desire and correct answer. German silver has high resistance to electricity, hence are perfect for use in heating coils.