A and B can complete a piece of work in 12 days and 18 days respectively. They work together for 4 days, after which A leaves the work. B continues alone for 6 days, and then C joins B. If C alone can complete the whole work in 9 days, find the total time (in days) taken to complete the work.
\(10\frac{2}{3}\)
Take the whole work as 36 units (LCM of 12, 18 and 9). Then A does 3 units/day, B does 2 units/day and C does 4 units/day.
A and B together for 4 days: 4 × (3 + 2) = 20 units.
B alone for 6 days: 6 × 2 = 12 units. Work done so far = 20 + 12 = 32 units, so 36 – 32 = 4 units remain.
B and C together do 2 + 4 = 6 units/day, so they need \(\frac{4}{6} = \frac{2}{3}\) day for the rest.
Total time = 4 + 6 + \(\frac{2}{3} = 10\frac{2}{3}\) days.
Check: \(20 + 12 + 6 \times \frac{2}{3} = 20 + 12 + 4 = 36\) units, which is the whole work.
Hence, \(10\frac{2}{3}\).
Similar Questions
Two people of equal efficiency working together can complete a task in 6 hours. How long would it take one person alone to complete the same task?
A, B, and C can complete a project alone in 12 days, 18 days, and 24 days, respectively. If they all work together for 4 days, what fraction of the project will remain incomplete?
A group of 6 identical workers can finish a task in 9 days. How many days will it take if only 3 of them work together to complete the same task?
Three friends, Arjun, Kabir, and Neha, can paint a fence in 12 hours, 6 hours, and 4 hours, respectively. If they work together, how long will they take to paint the fence?
Ram can do a job in x days. Mohan is twice as fast as Ram. Raghav is 50% more efficient than Mohan. If Ram, Mohan and Raghav together finish the job in 4 days, what is the value of x?
A can complete a piece of work in 12 days and B can complete the same work in 18 days. They start working together. After 4 days, A leaves the work. In how many more days will B finish the remaining work?
Important Questions from Work Efficiency
Five men and 2 boys can do in 30 days as much work as 7 men and 10 boys can do in 15 days. How many boys should join 40 men to do the same work in 4 days?
A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work further increased by 50%?
24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?
A and B together can do a piece of work in 4 days, B and C can do it in 6 days, A and C can do it in 8 days. Then A, B and C together can do the same work in :-
A can complete 50% of a work in 9 days and B can do 25% of the work in 9 days, if they work alone. If they work together then how much work (in percentage) can be completed in 6 days?
