Bissoy.com
Doctors Medicines MCQs Q&A

A, B, and C can do a piece of work in 12, 15, and 20 days respectively. A can do the work for 5 days after that B joined A and A works with his half efficiency. They both worked for 2 days together and after that C joined them and B works with 1 / 4 of his efficiency. They all worked together for 2 days and after that C left and A and B are working their normal efficiency. Then find In how many days A and B can complete the remaining work.

A, B, and C can do a piece of work in 12, 15, and 20 days respectively. A can do the work for 5 days after that B joined A and A works with his half efficiency. They both worked for 2 days together and after that C joined them and B works with 1 / 4 of his efficiency. They all worked together for 2 days and after that C left and A and B are working their normal efficiency. Then find In how many days A and B can complete the remaining work. Correct Answer 1 day

Given:

A can do a piece of work = 12 days

B can do a piece of work = 15 days

C can do a piece of work = 20 days

Concept used:

Total work = LCM

Work done in unit value of time is known as efficiency

Formula used:

Efficiency = total work / total days

Calculations:

Let the total work be x

∴ Efficiency of A = total work / total days = x / 12

∴ Efficiency of B = total work / total days = x / 15

∴ Efficiency of C = total work / total days = x / 20

∵ A can do the work for 5 days

∴ Work done by A = (x / 12) × 5 = 5x / 12

∵ After 5 days B joined A and A works with half of his efficiency for next 2 days

∴ Work done by A and B in one day = (x / 24) + (x / 15) = 13x / 120

∴ Work done by A and B in two days = 2 × (13x / 120) = 13x / 60

∵ After 5 days C joined A and B, B works with 1 / 4 of his efficiency for next 2 days

∴ Work done by A, B and C in one day = (x / 24) + (x / 60) + (x / 20) = 13x / 120

∴ Work done by A, B and C in two days = 2 × (13x / 120) = 13x / 60

Total work completed in 9 days = (5x / 12) + (13x / 60) + (13x / 60) = 51x / 60 = 17x / 20

∴ The remaining work = x – (17x / 20) = 3x / 20

∵ For remaining work C left and A and B work with their normal efficiency

∴ Work done by A and B in one day = (x / 12) + (x / 15) = 9x / 60 = 3x / 20

∴ Remaining work done by A and B = remaining work / efficiency

⇒ (3x / 20) ÷ (3x / 20) = 1 day

Alternate method:

Total work = LCM = 60

∴ Efficiency of A = total work / total days = 60 / 12 = 5

∴ Efficiency of B = total work / total days = 60 / 15 = 4

∴ Efficiency of C = total work / total days = 60 / 20 = 3

∵ A can do the work for 5 days

∴ Work done by A = 5 × 5 =25

∵ After 5 days B joined A and A works with half of his efficiency for next 2 days

∴ Work done by A and B in one day = (5 / 2) + 4 = 13 / 2

∴ Work done by A and B in two days = 2 × (13 / 2) = 13

∵ After 5 days C joined A and B, B works with 1 / 4 of his efficiency for next 2 days

∴ Work done by A, B and C in one day = (5 / 2) + 1 + 3 = 13 / 2

∴ Work done by A, B and C in two days = 2 × (13 / 2) = 13

Total work completed in 9 days = 25 + 13 + 13 = 51

∴ The remaining work = 60 – 51 = 9

∵ For remaining work C left and A and B work with their normal efficiency

∴ Work done by A and B in one day = 5 + 4 = 9

∴ Remaining work done by A and B = remaining work / efficiency

⇒ 9 / 9 = 1 day

Related Questions

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.
Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: M and N can complete the work in 10 and 20 days respectively. They started doing work together but after 4 days M left the work. In what time N can complete the remaining work? Quantity B: A and B can together complete the work in 12 days. A alone can complete the work in 30 days. If B works for first 4 days alone and then A joins the work, in how many days remaining work will be complete?
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?
A, B, and C can do a piece of work in 20 days, 30 days, and 15 days respectively. They start the work together but after 3 days they leave the work and the work is stopped for the next 15 days. After that D, E and F joined the work and did the work alternately and D started the remaining work. If D’s efficiency is twice A, E’s efficiency is half of B and F is equally efficient as C. So find in how many days D, E, and F complete the remaining work.
Amit can do a piece of work in 45 days, but Bharath can do the same work in 5 days less, than Amit, when working alone. Amit and Bharath both started the work together but Bharath left after some days and Amit finished the remaining work in 56 days with half of his efficiency but he did the work with Bharath with his complete efficiency. For how many days they had worked together?
Choose the correct option from the following Quantity I: If A and B can do a piece of work in 10 days, B and C in 12 days and if all three are together then said work is done in 8 days. In how many days would C and A complete the work if working together? Quantity II: A can do a piece of work in 2/5th of work in 10 days and B can do 1/2 of the same work in 8 days. If both of them are working together then in how many days would the work get completed?
Newton, Einstein, and Tesla working alone can do a piece of work in 20, 30, and 60 days respectively. All three of them start the work together, but after x days Newton leaves and then after y more days Einstein leaves and Tesla completes the remaining work. If Einstein had not left, Tesla and Einstein would have completed the remaining work in (y + 6) days after Newton had left. If both Newton and Einstein had stayed, the work would have been completed in (x + 6) days. What is the total number of days taken to complete the work?
What is the total number of employees in the company? Which of the following option is sufficient alone to find the answer? A) In the company, employees like either tea or coffee or cold drink. Out of the total employees, 25% like tea and 40% like coffee. Out of remaining employees, 20% like cold drink and remaining employees don’t like any of these drinks. B) Out of total employees 18% working in the marketing departments, 35% working in IT departments. From the remaining employees 25% working in HR departments and 45% working in content departments and remaining 141 are working in other departments. C) Employees working in the company is form state X, Y and Z. 20% of employees working in the company is from state X and from remaining 60% employees is from state Z and the remaining employees is from the state Y. D) 60% of the employees in the company are married and remaining employees are unmarried. The ratio of male and female unmarried employees is 4 : 5 and ratio of married male and female employees is 3 : 4.
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.
A can do a piece of work in 20 days and B can do the same piece of work in 30 days. A and B started the work together in the first 10 days A worked with half of his efficiency and so does B. Now in how many days does the remaining work get completed when both of them work with their full efficiency?