Bissoy.com
Doctors Medicines MCQs Q&A

Three friends A, B and C worked together to complete the work. A takes 4 days more to complete same work done by A and B. Work done by C in 4 days is equal to the work done by A in one day. Work done by B in 3 days is equal to the work done by C in 8 days. Find the time in which work will be completed if all three worked together.

Three friends A, B and C worked together to complete the work. A takes 4 days more to complete same work done by A and B. Work done by C in 4 days is equal to the work done by A in one day. Work done by B in 3 days is equal to the work done by C in 8 days. Find the time in which work will be completed if all three worked together. Correct Answer 120/23 days

Calculation:

Let number of hours taken by A, B and C to complete the work be a, b and c respectively.

⇒ 3/b = 8/c

⇒ 3c = 8b

⇒ 4/c = 1/a

⇒ c = 4a

⇒ b = 3a/2

⇒ 1/a + 1/b = 1/(a - 4)

⇒ 1/a + 2/3a = 1/(a - 4)

⇒ a  = 10

⇒ b = 15

⇒c = 40

(A + B + C)'s 1 hours work = 1/10 + 1/15 + 1/40 = 23/120

∴ Working together, A, B and C can complete the work in 120/23 days.

Important Points

Work done in a hours by person = a × persons 1 hour's work

Related Questions

P alone can complete the work in 20 days, Q alone can complete the work in 30 days while R alone can complete the work in 10 days. They start working in turns as P works on first day, Q on second day and R on third day, so on till sixth day. On seventh day, all three worked together to complete remaining work. Find the approx. time in which whole work is completed.
A piece of work can be completed by a man in 66 days. The same work can be completed by two women together in the same time and the same work can be completed by three kids together in the same time. If 1 man, 1 woman, and 1 kid work together then in how many days the work will be completed?
Three friends Adam, Eve and Kane who are working together working at different speed where Adam being the slowest and Kane being the Fastest. When Adam and Eve work together they take x days to finish a task. When Eve and Kane work together they take y days to finish a task. One of them, if he worked alone would take thrice as much time as it would take when all three work together. How much time would it take if all three worked together?
Paddy transplantation in Punjab is a very hard labor-intensive back-breaking job. In the transplant season, teams of special people swarm the entire rural landscape employed by the farmers and can be seen laboring away in the fields under the hot sweltering sun. Farmer Jagtar Singh has a full-time help at his sprawling farm who goes by the name of Hari, and who hails from Allahabad, UP. During the paddy transplant season, it is up to Hari to rope in his brothers, sons, and cousins from his native village to complete the task well in time. All his people are skillful and masters of the trade and equally efficient at their jobs. So, this past season, this is how the work went. Hari started the work and after 't' hours was joined in by his brother Jaggi. After another 't' hours, Neelu, their cousin, also jumped into the fray. So, after every 't' hours, 1 person kept on joining the team of already working men, and this process kept on continuing till the completion of the work. The last person worked for 't' hours. In the last season, the very same men had completed the same work working 2 shifts of 12 hours all of them working simultaneously owing to some peculiar weather conditions and time constraints. Jagtar Singh is a fair and just paymaster which is why he faces no labor shortage at this crucial time and which is why the whole 'Hari clan' are more than happy to work for him and are at his beck and call. He pays each of them individually proportional to the work done by them. This time around, Hari received 11 times as much as Surinder, his eldest son, who was the last person to join in. In how much time was the work completed?
Each question below is followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. P, Q and R together can complete a work in 12 days. All of them worked together for 6 days and then P left. How much time will Q and R together will take to complete the remaining work? I. If P completes a work in X number of days, then Q and R together complete the work in X number of days. II. After leaving the work, P completed another work in 10 days.
Puneet completes a work in 12 days and Rachna completes a work in 6 days. But Puneet worked only for 4 days and Rachna worked only for 2 days. The remaining work was done by Sahil and Sachin who alone can complete the work in 10 days and 6 days respectively. Ratio of the number of days for which Sahil and Sachin worked is 1 : 1. Find the total number of days for which Rachna, Sahil, and Sachin worked.
In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: A can do a piece of work in 10 days and B can do the same work in 15 days. They start working together and after 4 days, A left the work. Find in how many days the total work will be completed. Quantity B: P can do a piece of work in 15 days and Q can do the same work in 25 days. They start working together and after 5 days, Q left the work. Find in how many days the remaining work will gets completed.
A and B together can complete a work in 15 days while B and C together can complete the same work in 20 days. A worked for 8 days, then B worked for 10 days and C completed the remaining work in 3 days. In how many days C can complete the whole work alone?
Two friends Raj and Rohit work in a factory. If Rohit worked alone, he would need 8 hours more to complete the work than if they both worked together. now If Raj worked alone, it would need 4.5 hours more to complete the work than they both working together. what time would it take Raj alone to complete the work?
Rajeev is 4 times as efficient as Kamal and half as efficient as Vinod. A certain work was completed by all of them in 15 days, such that Rajeev worked alone for the first 3 days, then Rajeev and Kamal worked together for next 6 days, and all three of them worked together for the remaining days. In how many days can Rajeev do the work alone?