Question : A and B can do a piece of work in 15 days. B and C can do the same work in 10 days and A and C can do the same in 12 days. The time taken by A, B and C together to do the job is:
Option 1: 4 days
Option 2: 9 days
Option 3: 8 days
Option 4: 5 days
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Correct Answer: 8 days
Solution : Given: A and B can do a piece of work in 15 days. B and C can do the same work in 10 days also A and C can do the same in 12 days. (A + B) in 1 day can do $\frac{1}{15}$ part of the work (B + C) in 1 day can do $\frac{1}{10}$ part of the work (C + A) in 1 day can do $\frac{1}{12}$ part of the work So, the part of the work (A + B + C) can be done in 1 day, = $\frac{1}{2}(\frac{1}{15}+\frac{1}{10}+\frac{1}{12})$ = $\frac{1}{2}(\frac{4+6+5}{60})$ = $\frac{15}{120}$ Therefore, the time taken by A, B, and C together to do the job is $(\frac{1}{\frac{15}{120}})=\frac{120}{15}$ = 8 days Hence, the correct answer is 8 days.
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Question : A and B together can complete a work in 20 days. B and C together can complete the same work in 15 days. If A, B, and C all work together, then the same work gets completed in 10 days. How many days will A and C together take to complete the same work?
Option 1: 8 days
Option 2: 10 days
Option 3: 15 days
Option 4: 12 days
Question : A can complete a piece of work in 9 days. B and C can complete the same work in 12 days and 18 days respectively. If A, B, and C work together, then in how many days will they complete the work?
Option 1: 10 days
Option 2: 8 days
Option 3: 4 days
Option 4: 15 days
Question : A and B can do a piece of work in 10 days and 15 days, respectively. They worked together, but 5 days before the completion of the work, A left. In how many days was the work completed?
Option 1: 4
Option 2: 8
Option 3: 6
Option 4: 9
Question : A can do a piece of work in 12 days and B can do the same work in 15 days. If both do the work together, then in how many days will the work be completed?
Option 1: $7 \frac{2}{3}$
Option 2: $6 \frac{2}{3}$
Option 3: $5 \frac{2}{3}$
Option 4: $8 \frac{2}{3}$
Question : A and B working separately can do a piece of work in 9 and 15 days respectively. If they work on alternate days, starting with A, then the work will be completed in:
Option 2: 11 days
Option 3: 9 days
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