A job can be completed by 12 men in 12 days. How many extra days will be needed to complete the remaining job, if 6 men leave after working for 6 days?a)3b)6c)12d)24Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given:

- 12 men can complete a job in 12 days.
- 6 men left after 6 days.

To find:

- How many extra days will be needed to complete the remaining job?

Solution:

Let's assume that the total work is represented by the variable 'W'.

We know that 12 men can complete the job in 12 days, which means:

- 1 man can complete the job in 12 x 12 = 144 days (since he will be working alone)
- Therefore, the work done by 1 man in 1 day = W/144

Now, let's calculate the work done by 12 men in 6 days:

- Work done by 1 man in 1 day = W/144
- Work done by 12 men in 1 day = 12 x (W/144) = W/12
- Work done by 12 men in 6 days = (W/12) x 6 = W/2

So, after 6 days, 6 men leave, which means that only 6 men are left to complete the remaining work. Let's assume that they take 'x' extra days to complete the remaining work.

- Work done by 1 man in 1 day = W/144
- Work done by 6 men in 1 day = 6 x (W/144) = W/24
- Work done by 6 men in 'x' days = (W/24) x 'x' = Wx/24

Now, the total work done by 12 men and 6 men is equal to the total work:

- Work done by 12 men in 6 days + Work done by 6 men in 'x' days = W
- W/2 + Wx/24 = W
- 12W/24 + Wx/24 = W
- W(12 + x)/24 = W
- (12 + x)/24 = 1
- 12 + x = 24
- x = 12

Therefore, the extra days needed to complete the remaining work is 12 days.

Answer: Option B

Similar GATE Doubts

A contract is to be completed in 52 days and 125 identical robots were employed, each operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How many additional robots would be required to complete the work on time, if each robot is now operational for 8 hours a day?

For a given PERT activity, the standard deviation of the time needed to complete an activity is 3. If the optimistic time and the most likely time required to complete this activity are 8 and 12 minutes respectively. Find out the expected time in order to complete this activity.

Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. ow many matches will have to be held to complete the league round of matches?

Five teams have to compete in a league,with every team playing every other teamexactly once, before going to the nextround. How may matches will have to beheld to complete the league round ofmatches?

A buck converter, as shown in Figure (

Top Courses for GATE

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Other Engg Branches

Related Exams

Company