Here are some of the frequent and different questions asked in Time and Work are given.

A in some days ,B in some days then(A+B)=?.A, B, C separately finish work in some days  then(A+B+C)=?

1.A does a work in 10 days B does same work in 15 days.In how many days they together will do the same work?Similarly,In terms of three persons also will be asked with the same model

(AB)together,A alone finish work in some days then B alone?

2. A and B together complete a piece of work in 4 days.If A alone can complete the same work in 12 days,in how many days can B alone complete that work?

(AB)together ,(BC)together,(ABC)together finish work in some days, then (AC)together in?

3.A and B can do awork in 8 days,B and C can do the same work in 12 days .A,B and C together can finish it in 6 days.A and C together will do it in?
Also,A (or)B(or)C alone will do it in how many days?

A ‘s % efficient > B’s % efficient

4.A is 30% more efficient than B.How much time will they ,working together ,take to complete a job which A alone could have done in23 days?

Find  the remaining work:

5. A can finish a work in 18 days and B can do the same work in 15 days.B worked for 10 days and left the job.In how many days,A alone can finish the remaining work?

Problems on group persons: How many persons needed to finish the work?

6. Twenty four men can complete a work in sixteen days.Thirty two women can complete the same work in twenty four days. Sixteen men and sixteen women started working and worked for twelve days.How many more men are to be added to complete the remaining work in 2 days?

Question: Twenty four men can complete a work in sixteen days.Thirty two women can complete the same work in twenty four days. Sixteen men and sixteen women started working and worked for twelve days.How many more men are to be added to complete the remaining work in 2days?

Solution:

As per concept,
If(a person) finish the work in “n days” .
Then(a person 1day work )=[1/n],

If(24 men)finish the work in”16 days”
Then 24men 1 day work =1/16

From above find it for by (1man 1 day work),

24men 1 day work =1/16
Also we can write (24*1)men 1 day work=1/16
(1man 1 day work)= 1/(16*24)
(1man 1 day work)= 1/384
Therefore, Workdone by 1man in 1 day =1/384
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Similarly ,
We can find Workdone by 1woman in 1 day work 

Given that Workdone by 32 woman in 24days
As per concept,
If(a person) finish the work in “n days” .
Then(a person 1day work )=[1/n],

If(32 women)finish the work in”24 days”
Then 32 women 1 day work =1/24

From above find it for by (1woman 1 day work),

32women 1 day work =1/24
Also we can write ,
(32*1)women 1 day work=1/24
(1woman 1 day work)=1/(24*32)
(1woman 1 day work)=1/768
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Find the remaining work and No.of men in 2days for remaining work :

Given that, Sixteen men and sixteen women started working and worked for twelve days.How many more men are to be added to complete the remaining work in 2days?

So,First we have to find the remaining work.
Second we have to find how many men needed to finish remaining work in 2 days

Find work done by 16 men and 16 women for 12 days
Then 16 men and 16 women 12 day work[and means +]
W=(16 men + 16 women ) 12 day work
W=(16 *1man + 16*1 woman ) 1 2*1day work
W=16*12[1man1day work+1 woman 1day work]
W=16*12[(1/384)+(1/768)]
W=16*12[3/768]
W=3/4
Remaining work=1-(3/4)
Remaining work=1/4
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This remaining work 1/4 need to be finished in 2 days by adding more men with16 men and 16 women .
So,calculate 2 days work of 16 men and 16
W=(16 men + 16 women ) 2 day work
W=(16 *1man + 16*1 woman ) 2*1day work
W=16*2[3/768]
W=3/24
W=1/8
The remaining work need to to be finished in two days,
W=1/4-1/8
W=1/8
(1man 1 day work)= 1/384
384 men able to complete 1 work in 1 day.
For 1/8 work------>384/8=48
48 men able to complete 1/8 work in 1 day.
For 2 days--------->48/2=24
Therefore 24 men are required to finish the work.

“This problem is just a little bit different from previous time and work problems.In previous problems ,a work done by a person .Here a work done by more than one person. "

Question: 10 men and 15 women together can complete a work in 6 days.It takes 100 days for one man alone to complete the same work.How many days will be required for one woman alone to complete the same work?

Solution:

Consider, Workdone by 1man in 1 day=W[M]
Workdone by 1Woman in 1 day=W[W]

Given that,

10 men and 15 women =10M+15W
Therefore,Workdone by 10 men and 15 women in 1 day =W [10M+15W]
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1.Workdone by 10 men and 15 women in 1 day,
W[ 10M+15W]=1/6[Since 10 men and 15 women together can complete a work in 6 days ]
2.Workdone by 1man in 1 day,
W[M] =1/100 [one man alone complete the same work in 100 days]
3.Workdone by 10 man in 1 day,
W[10M]=10/100=1/10
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We can find ,how many days for one woman alone complete the same work using above.

W[10M+15W] =1/6
W[10M] + W[15W] =1/6
1/10 + W[15W] =1/6
W[15 W] =(1/6) –(1/10)[Take LCM and solve]
W[15 W]=(5-3)/30
W[15 W]=2/30
W[15 W]=1/15
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Workdone by 15 woman in 1 day =1/15
Workdone by 1 woman in 1 day,
(i.e)W[1W]= 1/(15*15)
W[1W]=1/225.
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Then as per concept,
If (a person 1day work )=[1/n],
then(a person) finish the work in “n days” .
So,one woman alone finish the work in 225 days

Question: A can finish a work in 18 days and B can do the same work in 15 days.B worked for 10 days and left the job.In how many days,A alone can finish the remaining work?

Solution:

Workdone by A in ‘1’ day =1/18
Workdone by B in ‘1’ day =1/15

From question:

B worked for 10 days and how many days A alone finish the remaining work,

Since B worked for 10 days,
Workdone by B in ‘10’ days =10/15

So we have to find the remaining work need to be finished,
Remaining work need to be finished =1-(10/15)=1-(2/3)=(3-2)/3=1/3
Remaining work=1/3
This remaining work (i.e) need to be finished by ‘A’alone which is asked in question

Given that ,

A can finish 1 work in 18 days .
But here remaining work is only 1/3.
So, A finish 1/3 work in 18*(1/3)=18/3=6 days

Therefore, A alone can finish the remaining work in 6 days.

Tips:

For example a person named B has ability to finish a work in 15 days,
Workdone by B in ‘1’ day =1/15
Workdone by B in ‘2’ days =2/15
Workdone by B in ‘3’days=3/15
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For example to find the remaining work:

To find the remaining work ,when B left the work in 2 days,
Workdone by B in ‘2’ days =2/15
Remaining work =1-(2/15)=13/15
Remaining work=13/15
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To find the remaining work ,when B left the work in 3days,
Workdone by B in ‘3’ days =3/15
Remaining work =1-(3/15)=12/15
Remaining work=12/15

Also see:

Time and Work
Different Problem on Time and Work

Hi friends,
I am happy to share this because it is my first post on aptitude.The solutions are look like big but after reading this it helps for exam preparation in simple way.Hope it helps………

Important Concepts in Time and Work:

If (a person) able to do 1work in “n” days,
                then (a person   1day work)=[1/n].
If (a person 1day work )=[1/n],
               then(a person) finish the work in “n days” .

Explaining  Time and Work with example:

Consider kannan(a person) able to do 1work in 1 day.Then kannan able to finish 5works in 5 days.But if1 work in 5 days means it is 1/5 as per concept.
Consider kavi able to do half work(i.e 1/2)  in 1 day.Then kavi able to finish 1 work in 2 days.So kavi able to finish 5 works in 10 days.But   if 1 work in 10days means it is 1/10 as per concept.

Kannan	Kavi
1st day = 1 work 2nd day = 1 work 3rd day= 1work 4th day= 1 work 5th day= 1 work	1st day = 1/2 work 6th day = 1/2 work 2nd day = 1/2work 7th day = 1/2 work 3rd day= 1/2work 8th day = 1/2 work 4th day= 1/2 work 9th day = 1/2 work 5th day= 1 /2work 10th day = 1/2 work
Total=5 works in 5 days	Total=5 work in 10 days

Why I am mentioning the above ?
Note that if  the ability of a person ability is less to finish the work then the days to finish the work wiil be more.

Some tips on Time and Work:

Try to convert the days into (a person 1day work)=[1/n].It will be mostly needed step in maximum problems in this type.

Problem on Time and Work:

Question:

A and B together can complete a piece of work in 4 days.If A alone can complete the same work in 12 days,in how many days can B alone complete that work?

Solution:

It was given that ,
A+B=4days ---------------------------------------------------------------->[Here and means +]
A=12days alone to  finish work
Therefore (A+B)one  day work------------------------------------------>[As given in concept]
W_(A+B)       =1/4 ------------------------------------------------------------>[Workdone   by  A+B in 1day]
W_A                =1/12----------------------------------------------------------->[Work done by   A alone in 1day]
Therefore,
W_{(A+B)  =}    W_A   + W_B  
1/4         =     1/12 +W_B
W_B           =    1/4  _  1/12-------------------------------------------------->[Work done by B alone in 1day]
W_B                 =1/6
Finally ,B alone can  complete the work in 6 days.

Anything  wrong? Comment below…

Also See:

Problem on Time and Work
Different Problem on Time and Work