Question

Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in y hours. In terms of x and y, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?

• A. $\frac{x}{x+y}$
• B. $\frac{y}{x+y}$
• C. $\frac{xy}{x+y}$
• D. $\frac{xy}{x-y}$
• E. $\frac{xy}{y-x}$

Answer 1

The correct option is E $\frac{xy}{y-x}$

Nails Produced per Hour by Machine $A=\frac{800}{y}$

Nails Produced per Hour by Machine $A$ and $B$ together $=\frac{800}{x}$

Let us assume Nails Produced per Hour by Machine $B=\frac{800}{B}$

$\Rightarrow \frac{800}{x}=\frac{800}{y}+\frac{800}{B}$

Solving we get,

$\Rightarrow B=\frac{xy}{y-x}$

Hence, the answer is $\left(E\right)$