Let's suppose that A and B takes $a$ and $b$ hours, respectively, to finish the same work while working alone.

Also, the question says that both can finish the work in $x$ hours, while working together.

Therefore, it can be inferred that A and B alone are going to take more time than $x$ hours to finish the work.

⇒ $a>x$ and also, $b>x$

It is also given that A takes y hours more than B to finish the work.

⇒ $a=b+y$

Substituting this value in the inequality above $(a>x)$, we get

$b+y>x$

⇒ $b>x-y$

And, if b is greater than $(x-y)$ than it will also be greater than $\frac{x-y}{2}$

⇒ $b>\frac{x-y}{2}$

And, $b$ is nothing but the time taken by B to finish the same work alone, i.e. Quantity A

Hence Quantity A is greater.

Option A

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