Bissoy.com
Doctors Medicines MCQs Q&A

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?

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? Correct Answer 30 days

Let Kamal take ‘x’ days to do the work alone

Kamal’s 1 day work = 1/x

Rajeev is 4 times as efficient as Kamal, so Rajeev’s 1 day work = 4/x

Rajeev is half as efficient as Vinod, so Vinod’s 1 day work = 8/x

It can be seen that Rajeev worked for all 15 days, Kamal worked for (15 – 3 =) 12 days and Vinod worked for (15 – 3 – 6 =) 6 days

Rajeev’s 15 days’ work = 60/x

Kamal’s 12 days’ work = 12/x

Vinod’s 6 days’ work = 48/x

Hence,

⇒ 60/x + 12/x + 48/x = 1

⇒ 120/x = 1

⇒ x = 120 days

⇒ 4/x = 4/120 = 1/30

∴ Rajeev will do the work alone in 30 days

Related Questions

A and B together work for 3 days, B then worked alone for 2 days, A then worked alone for 3 days and the work was finished. If A works for 8 days alone and B works for 4 days alone, the work will be finished. How many days will A alone work if B works for 5 days alone?
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.
Tom alone can complete the work in 30 days while Sam alone can complete the work in 40 days. Tom and Sam work for some days. Then Ron joins them to complete the remaining work. The remaining work gets completed in a day. Ron and Sam can complete half of the work in 60/11 days. How many days did Tom and Sam work?
Two workers P and Q started a job. For the first three hours only P works and then Q joins him to complete remaining work. When work completed it comes to know that P done 2/3rd of work and Q completed remaining work. After first four hours, there is still 3/5 of work is remaining. The number of days taken by alone P to complete work is what percent less than number of days taken by alone Q to complete the work?
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?
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?
X stars a certain work and after he completes exactly half the work, he leaves and Y takes up the remaining work and it takes a total of 45 days for the work to be completed this way. If X and Y working together can complete the work in 20 days, and Y is slower than X. Then, find the number of days in which the work will be completed, if X alone first works on exactly one-third, after which Y alone completes the rest of the work?
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.
Simplify the value of $$\frac{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} \times {\text{0}}{\text{.3}} - {\text{3}} \times 0.9 \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}}}}{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} - 0.9 \times {\text{0}}{\text{.2}} - {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}} - 0.3 \times 0.9}} = ?$$
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.