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Two persons having different productivity of labour, working together can reap a field in 2 days. If one-third of the field was reaped by the first man and rest by the other one working alternatively took 4 days. How long did it take for the faster person to reap the whole field working alone?

a) 3
b) 6
c) 8
d) 12

Answer: a
Explanation: Total efficiency of two persons = 50% [As they complete work in 2 days]
First Person completes work = $$\frac{1}{3}$$ = 33.33% [In 2 days]
Rest work will be completed by Second man = $$\frac{2}{3}$$ = 66.66% [In 2 days]
So, efficiency of second person is greater.
Efficiency of second person = $$\frac{{66.66}}{2}$$  = 33.33% per day
Then, Second person will complete whole work in,
= $$\frac{{100}}{{33.33}}$$  = 3 days.

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