Wednesday, 13 April 2016

[Q] Time and Work Tricks - 1

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".


Q. 1)

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.
Answer: (A)

Q. 2)

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.
Answer: (D)

Q. 3)

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
Answer: (D)


Q. 4)

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
Answer: (B)
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.

Q. 5)

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.
Answer: (C)

Q. 6)

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
Answer: (D)
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.

Q. 7)

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
Answer: (C)

Q. 8)

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
Answer: (A)

Q. 9)


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
Answer: (B)

Q. 10)


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
Answer: (D)


Q. 11)


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
Answer: (D)


If you have any doubts in this article, please drop a comment.
Keep reading :)


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43 comments:

  1. Qstn 6th is wrong nd the answer is c 115 min..

    ReplyDelete
    Replies
    1. thanks for pointing it out :)
      updated...

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    2. Plzz sir update the qustns relating to the volume in pipe nd cistern...

      Delete
  2. Which post is best in cgl for girls

    ReplyDelete
    Replies
    1. CSS - If you want to live in Delhi throughout your career.
      MEA - If you can manage foreign trips.

      Delete
  3. sir why u have taken 120 in qus3 ??

    ReplyDelete
  4. This is really a cool trick.. Awesome..

    ReplyDelete
  5. Hi, sir question no 6 main 57 last logic clear nai hua pls explain

    ReplyDelete
    Replies
    1. 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.

      Delete
    2. We can just consider Work done by A & B is 1/20-1/30 = 1/60
      That is work done by A & B in 2 min is 1/60 th part.
      Now, total work takes 120 min.

      Correct me if I am wrong.

      Delete
    3. if this site is still active?? its wonderfull

      Delete
  6. sir its a humble request to please post alternate time and work concept mujhe bataye please

    ReplyDelete
    Replies
    1. 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.

      Delete
  7. sir, can u add some posts related to syllogism soon?
    thanks for all ur wonderful shortcuts.

    ReplyDelete
  8. q.no 11 we need A+B not A+B+C.

    ReplyDelete
    Replies
    1. updated...SSC has removed official keys of 2014, hence not able to verify the answers. Thanks again :)

      Delete
  9. question 7 me hqlf work pucha hai...to i think answer option c hona chahiye...please correct me if i am wrong !!

    ReplyDelete
    Replies
    1. updated...SSC has removed official keys of 2014, hence not able to verify the answers. Thanks again :)

      Delete
  10. Sir in question 5 time is coming in the ration 12:15:4 after simplifying and LCM is coming 60 but we getting wrong answer. Why you took 15?

    ReplyDelete
    Replies
    1. You can take LCM = 60 and the answer wont change
      Efficiency of first pipe = 60/3 = +20 units
      Efficiency of second pipe = 60/3.75 = +16 units
      Efficiency of third pipe = 60/1 = -60 units
      Efficiency of all the three pipes = 20 + 16 – 60 = -24 units
      If all the pipes are opened, it will take 60/24 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.
      Now 5/4 = 1 + 1/4 = 1 hour and (1/4)*60 minutes = 1 hour and 15 minutes

      Delete
  11. In ques7,lcm 240 kaise aaya. Humne kis kis ko consider kia aur kyu?

    ReplyDelete
    Replies
    1. 40, 60 aur 80 ka LCM
      Just take the LCM of the values that are in front of you. Don't invest much time in picking appropriate numbers to find the LCM.

      Delete
  12. sir in q10 after solving the eq my ans is not coming 6 hrs.

    ReplyDelete
    Replies
    1. By mistake I had written 3.5, instead of 4.5. Please check the equation again.

      Delete
  13. yes sir done..!! :)

    ReplyDelete
  14. sir question no 11 ka koi aur chota jugaad nahi hai kya :P

    ReplyDelete
  15. Sir! Great job... :)

    ReplyDelete
  16. Loads of thanks to you sir....

    ReplyDelete
  17. really very helpful blog sir.thanks a lot....to you
    sir question number 3 me total work 120 hoga ya 60

    ReplyDelete
    Replies
    1. answer same aayega kuch bhi lo...waise haan, LCM 60 aayega...

      Delete
  18. In q8, if we take lcm =56 instead of 112, the answer doesn't match. What is the best way to take the lcm?

    ReplyDelete
  19. Sir, in question 8 how we got total work unit as 112 ? Can u please explain…

    ReplyDelete
    Replies
    1. take work = 56 and you will get the same answer. I messed up with the calculations...

      Delete
  20. sir please explain question 11 you have taken 2x days for c it , please explain that

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  21. sir please explain these two questions approach confused with hour and day.......

    1. while working 7 hrs a day A alone can complete a work in 6 days and B alone in 8 days . In what time would they complete it together working 8 hours a day?

    a) 3 days b)4 days c)2.5 days d)3.6 days

    2. A and B can do a piece of work in 8 days , B and C can do it in 24 days, while C and A can do it in 8+4/7 . In how many days C can do it alone ?
    a)60 days b)40 days c)30 days d)10 days
    in 2 nd question calculation of total work

    ReplyDelete
  22. sir please help me with above questions

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  23. Sir in question number 3 how total work is 120 units.if i calculate lcm of 15,12 and 10. i am getting lcm 60

    ReplyDelete
  24. Hi Prashant,
    Q.NO 7 must have ans d)(11)1/13 . clearly ratio 2m=3w=4c so we can take 10m+10w+10c=65/3men so 40*6/(65/3)=(11)1/13 months

    ReplyDelete