Question : 5 men can complete a work in 12 days, and 6 women can complete the same work in 20 days. In how many days can 1 man and 1 woman together complete this work?
Option 1: 120 days
Option 2: 32 days
Option 3: 40 days
Option 4: 60 days
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Correct Answer: 40 days
Solution : Given, 5 men can complete a work in 12 days, and 6 women can complete the same work in 20 days. We know, If A does $x$ amount of work in a day and B does $y$ amount of work in a day, then the total work done by both together, in a day = $\frac1x+\frac1y$ Work done by 1 man in a day $=\frac{1}{12×5}=\frac{1}{60}$ Work done by 1 woman in a day $=\frac{1}{6×20}=\frac{1}{120}$ Work done by 1 man and 1 woman in a day $=\frac{1}{60}+\frac{1}{120}=\frac{3}{120}=\frac{1}{40}$ So, the number of days in which 1 man and 1 woman together can complete the work is 40. Hence, the correct answer is 40 days.
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Question : A, B, and C together can complete a work in 5 days. A and B together can complete the same work in 6 days. C alone can finish the same work in how many days?
Option 1: 60 days
Option 2: 30 days
Option 3: 15 days
Option 4: 20 days
Question : A and B together complete a work in 20 days, B and C together complete the same work in 30 days, and C and A together complete the same work in 24 days. In how many days A, B, and C together can complete the same work?
Option 1: 8 days
Option 2: 16 days
Option 3: 12 days
Option 4: 15 days
Question : A can complete 25% of a work in 10 days. B can complete 40% of the same work in 16 days. In how many days will A and B together complete twice the work mentioned above?
Option 1: 20
Option 2: 40
Option 3: 60
Option 4: 50
Question : X and Y together can do a work in 10 days. Y and Z together can do the same work in 15 days. Z and X together can do the same work in 12 days. In how many days can Z alone do the same work?
Option 1: 80 days
Option 2: 60 days
Option 4: 50 days
Question : $\mathrm{N}_1$ alone can do 20% of a piece of work in 6 days, $\mathrm{N}_2$ alone can do 20% of the same work in 4 days, and $\mathrm{N}_3$ alone can do 50% of the same work in 12 days. In how many days can they complete the work, if all of them work together?
Option 1: 10 days
Option 2: $\frac{120}{13}$ days
Option 3: 8 days
Option 4: $\frac{120}{17}$ days
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