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# Time & Work

1.

A can do a work in 24 days and B can complete the same work in 12 days. In how many days the work will be completed if both work together?

A completes the work in 24 days. A's one day work will be 1/24 of the work.
B's one day work will be 1/12 of the work.
Both work together, in one day, 1/24 + 1/12 of the work will get over.
In one day 36/288 of the work will get over. Which means the work will get over in 288/36 days.
The work will get completed in 8 days.

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2.

Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B and C work together to complete the job?

Given that A and B can complete the work in 6 days A + B will do 1/6 of the work in 1 day => A + B = 1/6 ---> (1)
B and C can do the same job in 10 days, B + C will do 1/10 of the work in 1 day => B + C = 1/10 ---> (2)
C and A will do the same job in 7.5 days i.e., 15/2 days C + A will do 2/15 of the work in 1 day => C+ A = 2/15 ---> (3)
Adding all the above three equation we get 2 ( A + B + C ) = 1/6 + 1/10 + 2 /15 = 5/30 + 3/ 30 + 4 / 30 = 12 / 30 => A + B + C = 6 / 30 = 1 / 5
In one day A, B and C can finish 1/5 of the work => working together they will finish the work in 5 days.

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3.

A can do a work in 45 days and B can complete the same work in 36 days. In how many days the work will be completed if both work together?

A completes the work in 45 days. A's one day work will be 1/45 of the work.
B's one day work will be 1/36 of the work.
Both work together, in one day, 1/45 + 1/36 of the work will get over.
In one day 81/1620 of the work will get over.
Which means the work will get over in 1620/81 days. The work will get completed in 20 days.

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4.

A completes 60% of a task in 15 days and then takes the help of B and C. B is 50% as efficient as A is and C is 50% as efficient as B is. In how many more days will they complete the work?

A completes 60% of the task in 15 days i.e., he completes 4% of the task in a day.
B is 50% as efficient as A is, therefore, B will complete 2% of the task in a day.
C is 50% as efficient as B is, therefore, C will complete 1% of the task in a day.
Together, A, B and C will complete 4 + 2 + 1 = 7% of the work in a day.
They have another 40% of the task to be completed. Therefore, they will take 40 / 7 more days to complete the task.

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5.

A can do a work in 30 days and B can complete the same work in 45 days. In how many days the work will be completed if both work together?