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Bunuel
A mathematics professor can grade 20 exam papers in one day. How long will it take him to grade 30 papers if he is joined a colleague grading twice as fast?

A. 1/2 day
B. 3/4 day
C. 1 day
D. 3/2 days
E. 2 days

Efficiency of 1st professor = 20 papers/day
Efficiency of 2nd professor = 40 papers/day

Combined efficiency of 1st & 2nd Professor is 60 papers/day

Quote:
How long will it take him to grade 30 papers

Time taken by the 2 professors to grade 30 papers is \(\frac{30}{60}\) = \(\frac{1}{2}\) days..

Thus, the correct , answer must be (A) \(\frac{1}{2}\) days...
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individually they have 20 and 40 papers in a days
together they can have 60 papers in 1 days ... do for 30 it required 1/2 day ...
A is the answer
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In the problem it is mentioned that he can grade 20 papers in a day. So rate at which work is done by this professor is 20 paper per day.
He is joined by a professor who is twice as fast as him, so his rate would be 40 paper per day.

Combined they can grade 20 + 40 = 60 paper per day. So 30 papers could be graded in 30/60 days = 1/2 day
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A mathematics professor can grade 20 exam papers in one day.

His colleague grading twice as fast: 40 exam papers in one day

Working together: 20 + 40 = 60 papers one day.

Work required to be done: 30 papers.

Time required: \(\frac{1}{2}\) day.

Answer A
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