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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