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) x/(x+y)(B) y/(x+y)(C) xy/(x+y)(D) xy/(x-y)(E) xy/(y-x)

Answer 1

Answer: E.
`(xy)/(y-x)`

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 =
`(1)/(x)`

Working alone at its constant rate, Machine A produces 800 nails in y hours.

The rate of work by Machines A =
`(1)/(y)`

Let t be the time taken by Machine B to complete the whole work .

The rate of work by Machines B will be :-

`(1)/(t)=(1)/(x)-(1)/(y)\\\\\Rightarrow\ (1)/(t)=(y-x)/(xy)\\\\\Rightarrow\ t= (xy)/(y-x)`

Hence, the expression for hours taken by Machine B, working alone at its constant rate, to produce 800 nails :
`(xy)/(y-x)`