Answer: E. [tex]\dfrac{xy}{y-x}[/tex]
Step-by-step explanation:
Given : Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours.
Taking whole job as 1.
The rate of Machines A and B working together = [tex]\dfrac{1}{x}[/tex]
Working alone at its constant rate, Machine A produces 800 nails in y hours.
The rate of work by Machines A = [tex]\dfrac{1}{y}[/tex]
Let t be the time taken by Machine B to complete the whole work .
The rate of work by Machines B will be :-
[tex]\dfrac{1}{t}=\dfrac{1}{x}-\dfrac{1}{y}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{y-x}{xy}\\\\\Rightarrow\ t= \dfrac{xy}{y-x}[/tex]
Hence, the expression for hours taken by Machine B, working alone at its constant rate, to produce 800 nails : [tex]\dfrac{xy}{y-x}[/tex]
