Question for Practice Questions Level 2: Time & Work - 1
Try yourself:A and B work together for 8 days to complete a piece of work and B and C work together for 12 days to complete the same work. C alone can complete the work in 24 days and A is twice as efficient as B. How much time does it take to complete the work if all the three work together?
Explanation
1/A + 1/B = 1/8 ... (i)
1/B + 1/C = 1/12 ... (ii)
1/C = 1/24 ... (iii)
On solving, we get A = 12, B = 24 and C = 24
Therefore, 1/A + 1/B + 1/C = 1/6
All three together can complete the work in 6 days.
Question for Practice Questions Level 2: Time & Work - 1
Try yourself:A, B and C can do a piece of work in 20, 30 and 40 days, respectively. A and C started the work and B joined 4 days later. A left 8 days before the completion of work and C was also absent for 5 days in between. How many days will it take for the work to be completed?
Explanation
Assume that it takes 'd' days for the work to be completed.
A works for (d - 8) days,
B works for (d - 4) days,
C works for (d - 5) days.
6d - 48 + 4d - 16 + 3d - 15 = 120
13d = 199
d = days
Question for Practice Questions Level 2: Time & Work - 1
Try yourself:A group of employees is working on a project. If 10 more employees join them, then the project will be completed in of the time. If the work has to be completed in 1/3 of the time, then how many more employees have to join?
Explanation
Let M be number of employees present initially and d be the number of days taken by M employees to complete the work.
Md = (M + 10) 2/3 d
Solving, M = 20
To complete the work in 1/3 of the time, the number of employees should be 3 times (60).
So, 40 more employees have to join.
Question for Practice Questions Level 2: Time & Work - 1
Try yourself:A can do a piece of work in 20 days, working 8 hours a day and B can do the same work in 30 days, working 10 hours a day. If both A and B work together for 5 hours a day, how many days will they take to complete the same work?
Question for Practice Questions Level 2: Time & Work - 1
Try yourself:A and B together can complete a piece of work in 25 days. B and C together can complete the same work in 30 days. How many days would A and C take to complete the work?
Explanation
A and B can do 1/25 th of the work in 1 day.
B and C can do 1/30th of the work in 1 day.
From this, we cannot say anything about A and C.
Question for Practice Questions Level 2: Time & Work - 1
Try yourself:The amount of work done by a man on nth day after starting a piece of work is n times the amount of work that can be done on the first day. If 8 men start the work, it can be completed in 10 days. How many men should work if the work has to be completed in 4 days?
Explanation
Let each of the 8 men do x units of work on the first day.
Total work done = 8(x + 2x + 3x + 4x + 5x + 6x + 7x + 8x + 9x + 10x) = 440x
To do the same 440x units work in 4 days, let n men be required.
So, n(x + 2x + 3x + 4x) = 440x
⇒ n = 44
Question for Practice Questions Level 2: Time & Work - 1
Try yourself:A man started a piece of work on the first day. The second day, one more person joined him. The next day, one more person joined. Everyday, one new person joined until the work got completed. If the work was completed in 15 days, how many days would 10 men take to complete the same work, given that they worked regularly and efficiency of all men is the same?
Explanation
Let one day work of a man = x units
∵1st day = x
2nd day = 2x
……………..
……………
15th day = 15x
Total work done in 15 days = x + 2x + 3x + ... + 15x = 120x
So, time taken to complete 120x work by 10 men is 120x/10x = 12 days
Question for Practice Questions Level 2: Time & Work - 1
Try yourself:If 300 men could do a piece of work in 16 days, then how many men would do 1/4 of the same work in 15 days?
Explanation
300 men do 1 work in 16 days.
So, M_{1} = 300, D_{1} = 16, W_{1} = 1
Let y men do 1/4 work in 15 days.
Then, M_{2} = y, D_{2} = 15, W_{2} = 1/4
According to the formula:
M_{1}D_{1}W_{2} = M_{2}D_{2}W_{1}
300 x 16 x (1/4) = y x 15 x 1
Question for Practice Questions Level 2: Time & Work - 1
Try yourself:A alone can finish a piece of work in 12 days and B alone can do it in 18 days. If they work together and finish it, then out of total wages of Rs. 50, A will get
Explanation
A can finish the work in 12 days.
B can finish the work in 18 days.
∴ Ratio of their one-day work = 1/12 : 1/18 = 3 : 2
∴ If they work together and finish the work, they get the assigned amount in the ratio 3 : 2. That is, A will get Rs. 30 and B will get Rs. 20 (∵ total amount = Rs. 50).
Question for Practice Questions Level 2: Time & Work - 1
Try yourself:Two inlet pipes A and B can fill a tank in 24 hours and 30 hours, respectively. An outlet pipe C can empty the tank in 60 hours. The pipe C is continuously open and the pipes A and B work on alternate hours, starting with A. How much time does it take to fill the tank?