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**Hint:**Since we are given the percentage composition of the metal and Sulphur in the compound, we can say that the total mass will be $100grams$ and hence the mass of zinc will be equal to its percentage composition. To find the ratio of atoms, find the ratio of number of moles in the given species.

**Complete step by step answer:**

In the question, we have been given the value of the mass percentage of zinc as \[67.1\% \] by mass.

This means that \[67.1gram\] of zinc will be present in $100grams$ of the total compound.

Given Mass of the $Zn$ is $67.1grams$

From this we get mass of $S$ which will be: $Total\,mass - Mass\,of\,zinc$

Substituting the values, we get:

$100 - 67.1 = 32.9grams$

Now calculating the ratio of mass zinc and Sulphur

$Zn:S::67.1:32.9$

As we know that the molecular weight of zinc is $65.3$

And Molecular weight of Sulphur is $32$

Now calculating moles of zinc and Sulphur

$Moles = \dfrac{{Given\,mass}}{{molecular\,mass}}$

Substituting this value, in the ratio formula, we get:

$Zn:S =

\dfrac{{\dfrac{{mass\,of\,zinc}}{{molecular\,mass\,of\,zinc}}}}{{\dfrac{{mass\,of\,Sulphur}}{{molecular\,

mass\,of\,sulphur}}}}$

Substituting the values, we get:

$Zn:S = \dfrac{{\dfrac{{67.1}}{{65.3}}}}{{\dfrac{{32.9}}{{32}}}}$

Solving this value, we get the ratio as $1:1$

As per question the asked $x + y$ value is

comparing $x:y$ with $1:1$

Hence $x = 1$

$y = 1$

\[x + y = 1 + 1 = 2\]

**Note:**Law of constant proportion states that two elements combine in a fixed ratio when they have to form a molecule. Hence whenever Zinc and sulphide combine is the ratio of one is to one, they will form the same molecule everytime.

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