Bissoy.com
Doctors Medicines MCQs Q&A

Abdul can complete a work in 6 days. Bhide master can complete the same work in 10 days. Champak chacha can do it in 15 days. On day 1, only Champak chacha works. On day 2, both Champak chacha and Bhide master work together. On day 3, both Champak chacha and Abdul work together. After 3 days this cycle repeats. In how many days will the work get completed? 

Abdul can complete a work in 6 days. Bhide master can complete the same work in 10 days. Champak chacha can do it in 15 days. On day 1, only Champak chacha works. On day 2, both Champak chacha and Bhide master work together. On day 3, both Champak chacha and Abdul work together. After 3 days this cycle repeats. In how many days will the work get completed?  Correct Answer 7

Given:

Time taken by Abdul = 6 days

Time taken by Bhide Master = 10 days

Time taken by Champak Chacha = 15 days

Concept:

Total Work = Efficiency × time

Calculation:

Let the total work be LCM of (6, 10, 15) i.e 30 units

Efficiency of Abdul = 30/6 = 5 unit/day

Efficiency of Bhide Master = 30/10 = 3 unit/day

Efficiency of Champak Chacha = 30/15 = 2 unit/day

Total work done on day 1 by Champak Chacha = 2 units

Total work done on day 2 by Champak Chacha and Bhide Master = (2 + 3) = 5 units

Total work done on day 3 by Champak Chacha and Abdul = (2 + 5) = 7 units

So total work done in first 3 days = 2 + 5 + 7 = 14 units

This process will repeat again for 3 days

So, total work in next 3 days = 14 units

Total work till 6 days = 14 + 14 = 28 units 

On day 7, Champak Chacha will do 2 unit work alone

So total work till 7 days = 28 + 2 = 30 units 

∴ The required time is 7 days.

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.
P alone can complete the work in 12 days and Q alone can complete the work in 24 days. If P works alone for the first day and Q alone works for second day, after second day P and Q works together for next 5 days. After 7 days, R who has same work efficiency as Q, joins P and Q. In how many days, work will be 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?
A and B can do a piece of work in 30 days and 45 days respectively. They work together for 10 days and after that A goes on leave for 10 days and B works on every alternate day for the next 10 days and then goes on leave for the next 10 days after which A starts the work on every alternate day for the next 10 days. After that A and B together complete the remaining work. Find in how many days the work was completed.
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?
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?
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: 20% of students prefer to speak both English and Hindi while 40% of students prefer to speak Hindi and 55% of students prefer to speak English. 1300 students don’t prefer to speak both English and Hindi. Find the difference between the number of students who speak only English and only Hindi. Quantity B: 10 men can complete the work in 20 days while 30 women can complete the work in 40 days. If 8 men and 30 women started the work and they work for 8 days then left the work. The remaining work will be completed by a certain number of women in 57.6 days. Find the number of women who completed the remaining work.
In a school, a Science project has been assigned to three students Rajat, Rohan, and Bishal and it was told that they should work together on that project. Working alone Rohan can finish the project in 20 days, it is also given that if Rajat and Bishal work on the project they will take 9 days to complete the project. Bishal alone can complete the project in 15 days. Rohan started working on the project from Monday but after 8 days he left and after that Rajat and Bishal started working on it but Bishal also left 6 days before completion of the work and Rajat completed the remaining project, in how many days will the project be completed and on which day will it be completed?
A, B, and C can do a piece of work in 24 days, 30 days, and 40 days respectively. They start to work together and after four days, 50% of the completed work is destroyed by the air thereafter, they work for 6 days and after that, 16.66% of the total completed work is destroyed by rain. Thereafter, B left the work and A, C worked with twice their efficiency, after how many days remaining work was completed by A and C.
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 40% of a work in 6 days and B can do 30% of the same work in 3 days. They started the work together but B left after 2 days and A continued to work. In how many days was the entire work completed? Quantity B: Type 1 workers are two-and-a-half times as efficient as Type 2 workers. If 12 Type 1 workers can complete a task in 10 days, how many days would it take 6 type 1 and 10 type 2 workers to complete the same task?