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by MBA.Aspirant » Fri Jul 22, 2011 5:16 am
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
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by Anurag@Gurome » Fri Jul 22, 2011 6:20 am
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?
Say X and Y manufacture n number of toys in 6 hours and 8 hours respectively.
Hence, in one day X and Y manufacture 4n and 3n number of toys respectively.
Hence, in one day Z manufactures [3n - (4n - 3n)] = 2n number of toys.

Thus, in 5 days, all three of them together manufactures 5*(2n + 3n + 4n) = 45n number of toys.

Therefore, 45n = 1125 ---> n = 25

Hence, in 5 days, X manufactures 5*(4n) = 5*4*25 = 500 toys.

The correct answer is D.
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by GMATGuruNY » Fri Jul 22, 2011 7:31 am
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.
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