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**Hint:**The relation between vapour density and molecular mass is as follows: Molecular mass is double that of vapour density i.e. molecular mass is equal to twice of vapour density. By using this relation we can find the molecular mass and then the molar mass of unknown metal.

**Complete step by step answer:**

First of all we will see what is the relation between vapour density and molecular mass of a compound.

The relation is as follows:

Molecular mass $ = 2 \times $Vapour density

In the question the vapour density of the compound is given as $50$. So its molecular mass will be twice of vapour density i.e. $100$.

Now let us consider the Symbol of the unknown metal be $M$ and its valency be as $n$.

So the formula of metal chloride will be as $MC{l_n}$.

In the question it is given that the in the metal chloride $71\% $ by weight chlorine is weight i.e.

$\dfrac{{{\text{n }} \times {\text{ atomic mass of chlorine}}}}{{{\text{Mass of metal chloride}}}} = \dfrac{{71}}{{100}}$

Mass of metal chloride is equal to the mass of chlorine multiplied by factor n plus the atomic mass of metal. Let the atomic mass of metal be $x$.

Then the mass of metal chloride will be $35.5n + x$.

Now we know that Molecular mass of metal chloride is $100$.

So, $35.5n + x = 100$

By putting the value of mass of metal chloride in the equation we will get the value of $n$ as:

$

\dfrac{{{\text{n }} \times {\text{ 35}}{\text{.5}}}}{{100}} = \dfrac{{71}}{{100}} \\

n = 2 \\

$

As we have calculated the value of $n$ so putting its value in an equation in which the variables are $x$ and $n$ we will get the value of $x$ as.

Now, we put the value of $n$ in the last equation then we will get the value of $x$ as:

$

35.5 \times 2 + x = 100 \\

x = 29 \\

$

By putting the value of $n$ we get the value of $x$ as $29$. So the atomic weight of metal will be $29$. And the metal chloride will be as: $MC{l_2}$in which the atomic mass of $M$ is $29$.

**So, the correct answer is Option A .**

**Note:**

Vapour density is defined as the density of a gas or substance relative to hydrogen at the same temperature and pressure i.e. mass of substance in a certain volume divided by the mass of hydrogen gas at the same volume.

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