From the question data, we gather that the total work done is N kg of marzipan and the total time is 10 hours. From this, we can conclude that the combined rate of working of the two machines =\( \frac{N }{ 10}\) kg of marzipan per hour.
We are to calculate the fraction of the work done by machine W of the total work done by both. Since both machines have worked for the same period of time, finding the ratio of the rates will be enough to answer the question.
From statement I alone, we know that machine W takes 25 hours to produce (\(\frac{N}{2}\)) kg of marzipan. This means, rate of Machine W = \(\frac{N}{50}\) kg of marzipan per hour.
From the question data, we already know the combined rate of both machines. Can we find the ratio of the rate of W to the rate of both? Yes, we can.
Statement I alone is sufficient. Answer options B, C, and E can be eliminated. The possible answer options at this stage are A or D.
From statement II alone, machine W produces \(\frac{N}{2}\) kg of marzipan in double the time it takes machine D alone to produce N kg of marzipan. This means that machine W would take 4 times the time taken by D to produce N kg of marzipan.
So, rate of W = ¼ rate of D. If the rate of D = 4d kg per hour, rate of W = d kg per hour.
Combined rate = 5d kg per hour = \(\frac{N }{10}\). Simplifying, we have d = \(\frac{N }{50}\) kg per hour. This was the same value given to us in statement I alone, which turned out to be sufficient.
Therefore, statement II alone is also sufficient. Answer option A can be eliminated.
The correct answer option is D
Hope that helps!
Aravind B T
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Crackverbal Prep Team
www.crackverbal.com