Carcass wrote:
Let the speed at which Andy and Ben do the work is A units/hour \& B units/hour respectively.
So, the time taken by Andy and Bob to finish the work would be $\frac{1}{\mathrm{~A$ hours \& $\frac{1}{\mathrm{~B$ hours respectively. ( $\because$ Speed \& Time are inversely proportional when Work is constant)
As we know that Andy and Ben together finish the work in ' $x$ ' houirs, so their combined speeds is $\frac{1}{x}$, we get $A+B=\frac{1}{x} \ldots$ (1) Also it is given that the time taken by Andy to finish the work alone is ' $y$ ' hours more than the time taken by Ben alone to finish the work, so we get $\frac{1}{A}-\frac{1}{B}=y \ldots . .(2)$
Subtracting equations (1) \& (2) we get $\frac{2}{B}=x-y \Rightarrow \frac{1}{B}=\frac{x-y}{2}$ which is equal to the time that Ben would take to finish the work alone.
Hence column (A) has same quantity as column (B), so the answer is (A).
Thank you, but when A + B = 1/x, shouldn't it be x = 1/(A+B)?