Rate

MBA.Aspirant wrote:In a given time, X can do as much more work than Y, as Y can do more than Z. In five days all three of them can manufacture 1125 toys. If X and Y manufacture the same number of toys in 6 hours and 8 hours respectively, how many toys does X manufacture in 5 days?

a) 540

b) 450

c) 375

d) 500

Plug in a number to determine the ratio of the rates.

Let work done by X in 6 hours = 24 units.
Rate for X = 24/6 = 4 units per hour.
Rate for Y = 24/8 = 3 units per hour.
Since X produces 1 more unit per hour than Y, we know that Y produces 1 more unit per hour than Z.
Thus, rate for Z = 3-1 = 2 units per hour.

Thus, the combined rates for X+Y+Z = 4+3+2 = 9 units per hour.
This means that of every 9 units produced, X produces 4.
Thus, X produces 4/9 of the 1125 toys.
Toys produced by X in 5 days = 4/9 * 1125 = 500.

The correct answer is A.