Bissoy.com
Doctors Medicines MCQs Q&A

Varun and Karun can do a piece of work in 18 days and 27 days respectively. Karun starts the work and Varun joined him after some days. The total work is completed in 15 days from the beginning. After how many days did Varun joined with Karun?

Varun and Karun can do a piece of work in 18 days and 27 days respectively. Karun starts the work and Varun joined him after some days. The total work is completed in 15 days from the beginning. After how many days did Varun joined with Karun? Correct Answer 7 days 

Given:

Varun and Karun can do a piece of work in 18 days and 27 days respectively.

Total work is completed in 15 days.

Concept Used:

If a person takes x days to complete a work, the part of the work completed by him in 1 day = 1/x

Calculations:

Consider, Varun joined after ‘x’ days.

So, the work can be divided into two parts:

First, when Karun works alone for x days.

Secondly, when they work together for (15 - x) days.

Hence, the total work becomes:

Karun’s x days' work + (Varun’s + Karun's) (15 – x) days' work = 1

⇒ (x/27) + (15 - x) = 1         

⇒ (2x/54) + (15 - x) = 1         

⇒ (2x/54) + (15 - x)(5/54) = 1                  

⇒ 2x + 5 × (15 - x) = 54

⇒ 2x + 75 - 5x = 54       

⇒ -3x = 54 - 75 

⇒ x = 21/3 = 7 days

∴ Varun joined with Karun after 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.
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.
X, Y and Z can do a piece of work in 46 days, 92 days and 23 days, respectively, X started the work. Y joined him after 2 days. If Z joined them after 8 days from the beginning then for how many days did X work?
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.
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?
A, B and C can complete a work in 20, 24 and 30 days respectively. All three of them starts together but after 4 days A leaves the job and B left the job 6 days before the work was completed. C completed the remaining work alone. In how many days was the total work completed?
A, B and C can complete a work in 10, 12 and 15 days respectively. All three of them starts together but after 2 days A leaves the job and B left the job 3 days before the work was completed. C completed the remaining work alone. In how many days was the total work completed?
10 men can do a piece of work in 65 days. If 1 man starts work and the next day 3 men joined him again the next day 5 men joined the group and next day 7 men joined the group and follow the same pattern, now find out in how many days the work will be completed?
John is twice as efficient as Johny and Johny can do a piece of work in 30 days. Johny started the work and after a few days, John joined him. They completed the work in 22 days. From the very beginning, for how many days did they work together?
A, B and C can finish a task in 42 days, 84 days and 28 days, respectively. A started the work. B joined him after 3 days. If C joined them after 5 days from the beginning, then for how many days did A work till the completion of the task?