**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.**

**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".**

__Note:__

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)**

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

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)**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)**

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.

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)**

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.

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)**

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)**

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)**

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)**

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 :)

Keep reading :)

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

ReplyDeletethanks for pointing it out :)

Deleteupdated...

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

DeleteWhich post is best in cgl for girls

ReplyDeleteCSS - If you want to live in Delhi throughout your career.

DeleteMEA - If you can manage foreign trips.

sir why u have taken 120 in qus3 ??

ReplyDeleteYou can take 60 as well. No issue...

Deletethnku sir

ReplyDeletethnku sir

ReplyDeletegeometry ki tricks more please

ReplyDeleteThis is really a cool trick.. Awesome..

ReplyDeleteHi, sir question no 6 main 57 last logic clear nai hua pls explain

ReplyDeleteWe 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.

DeleteWe can just consider Work done by A & B is 1/20-1/30 = 1/60

DeleteThat 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.

if this site is still active?? its wonderfull

Deletesir its a humble request to please post alternate time and work concept mujhe bataye please

ReplyDeleteWe 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.

Deletesir, can u add some posts related to syllogism soon?

ReplyDeletethanks for all ur wonderful shortcuts.

Thanks a lot sir. Awesome

ReplyDeleteq.no 11 we need A+B not A+B+C.

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

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

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

DeleteSir 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?

ReplyDeleteYou can take LCM = 60 and the answer wont change

DeleteEfficiency 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

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

ReplyDelete40, 60 aur 80 ka LCM

DeleteJust 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.

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

ReplyDeleteBy mistake I had written 3.5, instead of 4.5. Please check the equation again.

Deleteyes sir done..!! :)

ReplyDeletesir question no 11 ka koi aur chota jugaad nahi hai kya :P

ReplyDeleteSir! Great job... :)

ReplyDeleteLoads of thanks to you sir....

ReplyDeletereally very helpful blog sir.thanks a lot....to you

ReplyDeletesir question number 3 me total work 120 hoga ya 60

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

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

ReplyDeleteSir, in question 8 how we got total work unit as 112 ? Can u please explain…

ReplyDeletetake work = 56 and you will get the same answer. I messed up with the calculations...

Deletesir please explain question 11 you have taken 2x days for c it , please explain that

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

ReplyDelete1. 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

sir please help me with above questions

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

ReplyDeleteHi Prashant,

ReplyDeleteQ.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