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Time and Work is yet another easy topic and almost all the questions are predictable. Please go through the following solved examples and I am sure that 90% questions would be similar to these examples. Most probably I will complete Time and Work in 3 parts.
Note: In the complete Time and Work series, Efficiency would mean “Work Done in 1 day”, and efficiency has been denoted by small letters, e.g. “a” means “Efficiency of A”.
Let the total work be 8 units (because 8 is the LCM of 4 and 8)
Efficiency of x (Work done by x in 1 hour) = 8/4 = 2 units
Efficiency of y (Work done by y in 1 hour) = 8/8 = 1 unit
Work done by (x + y) in 1 hour = 3 units
3 units work in completed in 1 hour. Hence 8 units work will be completed in 8/3 hours or 160 minutes.
Let total work be 60 units (LCM of 10 and 12)
Raj completes the work in 12 days. Hence efficiency or per day work of Raj = 60/12 = 5 units
Raj and Ram take 10 days to complete the work, hence their efficiency = 60/10 = 6 units
Now Efficiency of Ram = (Efficiency of Raj and Ram) – (Efficiency of Raj) = 6 – 5 = 1 unit
That means Raj completes 1 unit of work per day. So to perform 60 units of work, he will take 60 days.
Let total work = 120 units
Efficiency of A + B = 120/15 = 8 units
Efficiency of B + C = 120/12 = 10 units
Efficiency of C + A = 120/10 = 12 units
Adding all the above 3 equations –
2 * (A + B + C) = 30
Efficiency of (A + B + C) = 15 units
Efficiency of B + C = 120/12 = 10 units
Hence Efficiency of A = Efficiency of (A + B + C) – Efficiency of (B + C) = 15 – 10 = 5 units
Hence time taken by A to do 120 units of work = 120/5 = 24 days
Let the total work be 16 units.
Efficiency of first pipe = 16/4 = +4 units
Efficiency of second pipe = 16/16 = -1 units [negative sign because this pipe is emptying the tank] When both the pipes are opened together, their efficiency = (+4) + (-1) = +3 units [The positive sign indicates that when both the pipes are opened together, their net result will fill the tank] 3 units of work is done in 1 hour
16 units of work is done in 16/3 hours
Note : In questions where one pipe is emptying the cistern while another is filling it, you must put a positive or negative sign before the efficiency. But in questions where both the pipes are emptying the cistern or both the pipes are filling the cistern, you can take the efficiency of both the pipes as positive.
Let the total work be 15 units.
Efficiency of first pipe = 15/3 = +5 units
Efficiency of second pipe = 15/3.75 = +4 units
Efficiency of third pipe = 15/1 = -15 units
Efficiency of all the three pipes = 5 + 4 – 15 = -6 units
If all the pipes are opened, it will take 15/6 or 5/2 hours to empty the cistern, but the cistern is already half empty, hence only 5/4 hours are required to empty it.
Let the total work = 60 units
Efficiency of A = 60/20 = +3 units
Efficiency of B = 60/30 = -2 units
Now total work to be performed is 60 units. When 57 units work is complete, A will take 1 more minute to add 3 units and hence will make it a total of 60 units.
Hence time taken to fill the tank = Time taken to perform 57 units of work + 1 minute
Now A and B are opened alternatively. That means for the first minute only A is opened, for the second minute A is closed and B is opened, then for third minute again B is closed and A is opened and so on.
So for each 2 minutes cycle, work done = Efficiency of A + Efficiency of B = +3 + (-2) = 1 unit
1 unit work is done in 2 minutes, so 57 units work is done in 114 minutes
Time taken to fill the tank = 114 + 1 = 115 minutes
Explanation : We have to perform a total of 60 units of work. For the 1st minute – A adds 3 units of work, but in the 2nd minute, B adds (-2) units of work and hence makes total work for 2 minutes = (+3) + (-2) = 1 unit. So effectively in 2 minutes, we are just adding 1 unit of work. Hence in 4 minutes, 2 units of work will be performed and in 6 minutes 3 units of work will be performed. Same sequence will continue till 57 units. As soon as 57 units of work is done (in 114 minutes), it will be A’s turn to do the work. A will add 3 units of work(in 1 minute) and hence take the total work from 57 units to 60 units. B won’t be needed any more.
Let the total work be 240 units.
40 men complete the work in 6 months. Hence 10 men can complete the work in 6*4 = 24 months. Hence, Efficiency of 10 men = 240/24 = 10 units
60 women complete the work in 6 months. Hence 10 women can complete the work in 6*6 = 36 months. Hence, Efficiency of 10 women = 240/36 = 20/3 units
80 boys complete the work in 6 months. Hence 10 boys can complete the work in 6*8 = 48 months. Hence, Efficiency of 10 boys = 240/48 = 5 units
Efficiency of 10 men + Efficiency of 10 women + Efficiency of 10 boys = 10 + 20/3 + 5 = 65/3 units
So, 10 men, 10 women and 10 boys complete 65/3 units of work in 1 month. To complete 120 units(half of the work), they will take = 120 * 3/65 = 72/13 months
Let the total work be 112 units and the efficiency of 1 man and 1 woman be m and w respectively
2m + w = 112/14 = 8
4w + 2m = 112/8 = 14
Solve the equations and you will get w = 2 and m = 3
Hence the wage of woman = 2/3 * 180 = Rs. 120
A and C complete 19/23 of the work. Hence B does 4/23 of the work
Amount paid to B = 4/23 * 575 = Rs. 100
Let A and B complete the work in x days
Then A will complete the work in (x + 8) days and B will complete the work in (x + 4.5) days. Now,
1/(x + 8) + 1/(x + 4.5) = 1/x
Solve the equation and you will get x = 6 hours
The question is same the previous one.
Let A, B and C take ‘x’ days to do the job. Then,
A takes (x + 6) days, B takes (x + 1) days and C taken 2x days
1/(x + 6) + 1/(x + 1) + 1/2x = 1/x
1/(x + 6) + 1/(x + 1) = 1/x – 1/2x
1/(x + 6) + 1/(x + 1) = 1/2x … (1)
Solve it and you will get x = 2/3
From equation (1) you can see that A and B take 2x days to complete the work
If you have any doubts in this article, please drop a comment.
Keep reading 🙂