Question : A and B working together can do a piece of work in $4\frac{1}{2}$ hours. B and C working together can do it in 3 hours. C and A working together can do it in $2\frac{1}{4}$ hours. All of them begin the work at the same time. Find how much time they will take to finish the piece of work.
Option 1: 3 hours
Option 2: 2 hours
Option 3: 2.5 hours
Option 4: 3.25 hours
Correct Answer: 2 hours
Solution : Amount of work done by A and B in 1 hour = $\frac{2}{9}$ Amount of work done by B and C in 1 hour = $\frac{1}{3}$ Amount of work done by A and C in 1 hour = $\frac{4}{9}$ Adding all the equations, we have: ⇒ 2 × (A + B + C)'s 1 hour work = $\frac{2}{9}+\frac{1}{3}+\frac{4}{9}$ ⇒ 2 × (A + B + C)'s 1 hour work = $\frac{2+3+4}{9}=1$ ⇒ (A + B + C)'s 1 hour work = $\frac{1}{2}$ (A + B + C) can finish $\frac{1}{2}$ work in 1 hour. (A + B + C) can finish the total work in 2 hours. Hence, the correct answer is 2 hours.
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Question : A can do as much work as B and C together can do, A and B can do a piece of work in 9 hours 36 minutes and C can do it in 48 hours. The time (in hours) that B needs to do the work alone, is:
Option 1: 18 hours
Option 2: 24 hours
Option 3: 30 hours
Option 4: 12 hours
Question : Reena, Veena, and Vimla can do a work in 4 hours, 8 hours, and 12 hours, respectively. In how much time will they finish the work working together?
Option 1: $\frac{2}{11}$ hours
Option 2: $5\frac{2}{11}$ hours
Option 3: $3\frac{2}{11}$ hours
Option 4: $2\frac{2}{11}$ hours
Question : A can do $\frac{4}{5}$th of a work in 20 days and B can do $\frac{3}{4}$th of the same work in 15 days. They work together for 10 days. C alone completes the remaining work in 1 day. B and C together can complete $\frac{3}{4}$th of the same work in:
Option 1: 6 days
Option 2: 8 days
Option 3: 5 days
Option 4: 4 days
Question : A can do a certain piece of work in 2.4 times the number of days in which B and C together can do it. If A and B together can do the same piece of work in 27 days and C alone can do it in 75 days, then how many days will B take to do this piece of work alone?
Option 1: 54
Option 2: 48
Option 3: 45
Option 4: 42
Question : John can do a piece of work alone in 20 days, while Ravi can do the same piece of work alone in 28 days. In how many days can the duo complete the same work if they work together?
Option 1: $11 \frac{1}{3}$
Option 2: $12 \frac{2}{3}$
Option 3: $11 \frac{2}{3}$
Option 4: $12 \frac{1}{3}$
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