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Time and Work Shortcut Tricks Tips & Concept

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In all level competitive examinations questions on Time and Work have been asked. Due to limited number of types you can ensure your marks with minimum efforts. In these questions, time taken by one/two persons or groups in doing certain works,required number of persons for any work are commonly asked. Comparison of male, female, children works, time taken after distribution/change and questions based on efficiency (per cent of ratio) are also asked.

M = Number of men
D = Number of days
H = Number of hours per day
W = Amount of work

To Understand Concept Through Videos Visit Below link

Time And Work Shortcut Tricks Part 1 Video : Watch Now

Time And Work Shortcut Tricks Part 2 Video : Watch Now

Time And Work Shortcut Tricks Part 3 Video : Watch Now

Time And Work Shortcut Tricks Part 4 Video : Watch Now

Time And Work Shortcut Tricks Part 5 Video : Watch Now

Relationship between Men and Work.

More men  ==========⇒ can do  ==========⇒  More work

Less men  ===========⇒  can do  =========⇒  Less work

 

Relationship between Work and Time

More work  ==========⇒  takes  ==========⇒  More Time

Less work  ===========⇒  takes  ==========⇒  Less Time

 

  Relationship between Men and Time

More men  ===========⇒  can do in  =======⇒  Less Time

Less men  ============⇒  can do in  =======⇒  More Time

 

 

RULE 1 : If M1 men can finish W1 work in D1 days and M2 men can finish W2 work in D2 days then, Relation is

If M1 men finish W1 work in D1 days, working T1 timezeach day and M2 men finish W2 work in D2 days, working
T2 time each day, then

 

RULE 2 : If A completes a piece of work in ‘x’ days,and B completes the same work in ‘y’ days, then

Work done by A in 1 day =1/X, Work done by B in 1 day =1/Y

Work done by A and B in 1 day =

Total time taken to complete the work by A and B both =

 

 

RULE 3 : If A can do a work in ‘x’ days, B can do the same work in ‘y’ days, C can do the same work in ‘z’ days
then, total time taken by A, B and C to complete the work together

 

 

RULE 4 : If A alone can do a certain work in ‘x’ days and A and B together can do the same work in ‘y’ days,
then B alone can do the same work in

 

RULE 5 : If A and B can do a work in ‘x’ days, B and C can do the same work in ‘y’ days, C and A can do the same
work in ‘z’ days. Then total time taken, when A, B and C work together =

 

RULE 6 : Work of one day =Total work/Total no.of working days
Total work = (work of one day) × (total no. of working days)
Remaining work = 1 – (work done)
Work done by A = (Work done in 1 day by A) × (total no.of days worked by A

 

RULE 7 : If A can finish m/n part of the work in D days.Then,Total time taken to finish the work by A =

 

RULE 8 :

(i) If A can do a work in ‘x’ days and B can do the same work in ‘y’ days and when they started working
together, B left the work ‘m’ days before completion then total time taken to complete work is

(ii) A leaves the work ‘m’ days before its completion then total time taken to complete work is

 

RULE 9 : If A and B together can finish a certain work in ‘a’ days. They worked together for ‘b’ days and then ‘B’
(or A) left the work. A (or B) finished the rest work in ‘d’ days, then,Total time taken by A (or B) alone to complete the work

 

RULE 10 : If food is available for ‘a’ days for ‘A’ men at a certain place and after ‘b’ days. ‘B’ men join, then the
remaining food will serve total men for Required time =

 

Example:-

A and B can do a work in 12 days, B and C in 15 days and C and A in 20 days. If A, B and C work together, they will complete the work in

solution:-Using Rule 5, Time taken

 

 

Example:-

A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work?

solution:-Using Rule 2,

Here we are providing some cases of time & work and tricks to solve it. Hope this would be helpful to all aspirants.

Case 1 – A does a work in X days, B does a Work in Y days In how many days they will complete the work.

Question- A completes the work in 10 days and B completes the work in 15 days In how many days they will complete the work.

Efficiency method.
Efficiency of A =100/10 = 10%

Efficiency of B = 100/15 = 6.66%

Efficiency of A & B Together = 10+ 6.66 = 16.66%

So the time taken by A & B together to Complete the work will be 100/16.66 = 6 Days.

 

Case -2 A can do a work in X days and B can do it Y days, In how many days the work is completed if they work alternatively Started by A.

Efficienecy Method

A’s Efficiency = 10%

B’s Efficiency = 6.66%

A + B Efficiency = 16.66%

Work done by A and B in 2 days [ Remember 2 days because they are not working together but working alternatively] = 16.66%

So time taken by them to complete 100% work = 100/(16.66 = 6 [ but always remember multiply this by 2, Because 16.66% work is done by them in 2 days and not in 1 day.

Answer will be 6*2 = 12 days.

 

Case 3: A can do a work in X days, B can do the work Y days and A leaves after working Z days.

Question- A can do a work in 10 days and B can do it in 15 days, A works for 2 days and then leaves, In how many days will the work be completed?

Efficiency method 

A’s efficiency = 10%

B’s Efficiency = 6.66%

Total a+b = 16.66%

Work done by A and B together in 2 days = 16.66*2 = 33.33%

Work remaining = 66.66%

Time taken by B to complete 66.66% work = 66.66/6.666 = 10 days

Total time = 10+2 = 12 days

 

Case 4 : A can do a piece of Work in 10 days and B can do it in 15 days, In how many days will the work be completed if B leaves 2 days before the completion on work.

Efficiency method

A’s efficiency = 10%

B’s efficiency = 6.66%

Total = 16.66%

Work will be completed in 6 days

Work done in 4 days = 66.66%

Remaining = 33.33%

A will complete the remaining in = 33.33/10 = 3.33

Total = 4+3.33 = 7.33

 

Case 5: A can do a Work in X days B can Do it in Y days, In how many days The work will get completed if B leaves 2 days before the actual completion of work.

Question: A can do a work in 10 days B can do it in 15 days, In how many days The work will get completed if B leaves 2 days before the Actual Completion of Work. What is the difference between this Actual completion of work and Completion of Work?

Efficiency Method

A’s Efficiency = 10%

B’s Efficiency = 6.66%

Let the no. of days be x

 According to question

10x + 6.66(x-2) = 100 [ Work is always 100% in efficiency method ]

10x + 6.66x – 13.33 = 100

16.66x = 113.33

x = 113.33/16.66 = 6.8

Answer = 6.8 days

Some example problems on “LCM method for time and work problems”.

 Examples on “LCM method for time and work problems”

Example 1 :

A can do a piece of work in 8 days. B can do the same in 14 days. In how many days can the work be completed if A and B work together?

Solution :

Let us find LCM for the given no. of days “8” and “14”.

L.C.M of (8, 14) = 56

Therefore, total work = 56 units

A can do =  56 / 8 =  7 units/day

B can do = 56 / 14 =  4 units/day

(A + B) can do = 11 units per day

No. of days taken by (A+B) to complete  the same work

= 56 / 11 days

Example 5 :

A and B each working alone can do a work in 20 days and 15 days respectively. They started the work together, but B left after sometime and A finished the remaining work in 6 days. After how many days from the start, did B leave?

Solution :

Let us find LCM for the given no. of days “20” and “15”.

L.C.M of (20, 15) = 60 units

Therefore, total work = 60 units.

A can do = 60/20 = 3 units/day

B can do = 60/15 = 4 units/day

(A + B) can do = 7 units/day

The work done by A alone in 6 days = 6×3 = 18 units

Then the work done by (A+B) = 60 – 18  = 42 units

Initially, no. of days worked by A and B together

= 42/7 = 6 days

Example 8 :

Two pipes A and B can fill a tank in 16 minutes and 20 minutes respectively. If both the pipes are opened simultaneously, how long will it take to complete  fill the tank ?

Solution :

Let us find LCM of the given no. of minutes “16” and “20”

LCM of (16, 20) = 80

Total work = 80 units

A can fill = 80/16 = 5 units/min

B can fill = 80/20 = 4 units/min

(A+B) can fill = 9 units/min

No. of minutes taken by (A+B) to fill the tank

= 80/9 = 8 8/9 minutes

Example 9 :

Pipe A can fill a tank in 10 minutes. Pipe B can fill the same tank in 6 minutes. Pipe C can empty the tank in 12 minutes. If all of them work together, find the time taken to fill the empty tank.

Solution :

Let us find LCM of the given no. of minutes “10”, “6” and “12”

LCM of (10,6, 12) = 60

Total work = 60 units

A can fill = 60/10 = 6 units/min

B can fill = 60/6 = 10 units/min

(A+B) can fill = 16 units/min

C can empty = 60/12 = 5 units/min

If all of them work together,

(6 + 10 – 5)  =  11 units/min will be filled

If all of them work together, time taken to fill the empty tank

= 60/11 = 5 5/11 minutes

Formula required for Time and Work problems:

1.
 If ‘A’ can do the work in ‘n’ days , Then A’s one day work is 1/n

Tricks and Tips to solve Aptitude problems on Time and Work:

For Example, ‘A’ can do the work in 2 days, in one day he does half of the work (that is 1/2 work). It is simple, he can do the work in 2 days, that means first days he completed 50% of the work and second day finishing 50% of the work.

 

  1. If A’s 1 day’s work is 1/n, then A can finish the work in ‘n’ days.

Tricks and Tips to solve Aptitude problems on Time and Work

For example, A can finish the work in 3 days that means in first day he finishing 1/3rd of work, second day 1/3rd of work and third day 1/3rd of work.

Example Problems on Time and Work with solutions :

If A can finish a work in 2 days, B can finish the work in 3 days, then How many days together takes to finish the work?

General Method to solve Aptitude problems on Time and work:

  1. A) as per first formulae A’s one day work is 1/2
    B’s one day work is 1/3
    Now A and B work together in one day is (1/2)+(1/3) = 5/6

In one day A and B together work in one days is 5/6, So number of days they take together to finish the work ids 6/5. (as per second formula)

 

Tricks and tips to solve Aptitude problems on Time and Work:

a)If A can finish a work in x days, B can finish the work in y days, then and A and B together takes time to finish the work is xy/(x+y)

Check the answer with general method, A in 2 days, B in 3 days then A+B in 2*3/(2+3) = 6/5 days

  1. b)  If A can finish a work in x days, B can finish the work in y days, C and finish the work in z days then now together A&B&C finish the job in (x*y*z) /(xy+yz+zx)

Example problems on Time and Work with solutions :

  1. If A can finish a work in 3 days, B can finish the work in 6 days, then How many days together takes to finish the work?

Tips and Tricks to solve Time and work problems:

As per short cut method answer is 3*6/(3+6) = 18/9 = 2 days

One more trick to solve this type of Aptitude problems on time and work

Tricks and tips: Let Assume the job is 6 units (L.C.M of 3 and 6) (whatever it may be like making burgers or walking kilometers etc)

                A–> 3 days – > 6/3 = 2 units per day
B–> 6 days – > 6/6 = 1 unit per day
————————————————-
A+B -> 3 units per day        

The total job is 6 units, so  A and B together complete the work in 6/3 = 2 days.

  1. If A can finish a work in 12 hours, B can finish the same work in 15 hours, then How many minutes together takes to finish the work?

Tricks to solve Time and work problems Aptitude :

Let Assume the job is 60 units (L.C.M of 12 and 15)

                A– > 12 hours – > 60/12 = 5 units per day
B– >  15 hours – > 60/15 = 4 unit per day
————————————————-
A+B – > 9 units per day

The total job is 60 units, so  A and B together complete the work in 60/9 = 20/3 hours
= 20*60/3 minutes = 400 minutes

  1. A can do the work in 20 days, B can do the same work in 30 days. A,B and C together completed work in 10 days. In how many days C alone can do the work?Tricks and Tips to solve Time and work Aptitude problems:

                Total work = 60 units  (LCM of 20, 30,10)
A can do 3 units per day
B can do 2 units per day
A & B & C can do 6 units per day

                A– > 3
B— > 2
c- > ?
———
A + B + C –> 6

So C can do 1 unit per day (6-3-2)

Total job is 60 units , So C alone the complete job in 60/1 = 60 days

  1. A and B together can complete a work in 12 hours. B and C together can complete a same work in 15 hours. C and A together can complete a same work in 20 hours. In how many hours A & B & C together complete the work?
    A) 5                        B) 6                        C) 10                      D) 12

Time and work problems tricks:

                Total work = 60 units  (LCM of 12, 15,20)
A & B– > 60/12 = 5 units/day
B & C— > 60/15 = 4 units/day
C & A– > 60/20 = 3 units/day
———————————————————————–
2 (A + B + C) = 12 units/ day
= >(A + B + C) = 6 units/ day

Total job is 60 units. So A & B & C together complete the work in 60/6 = 10 days

  1. A and B together can complete a work in 12 hours. B and C together can complete a same work in 15 hours. C and A together can complete a same work in 20 hours. In How many hours B alone complete the task?

Tricks and Tips to solve Aptitude problems on Time and work with examples:

As the previous question answer (A + B + C) = 6 units/ day
B one day work is (A + B + C) one day work – C & A one day work
B = 6 – 3 = 3 units per day
Total job is 60 units. So B alone can complete the 60/3 = 20 days

Examples

 Q1. Ash can do a job in 10 days. Bali can do the same job in 5 days. In how many days they can complete the job if they work together?

  1. 6 days
  2. 3.33 days
  3. 7.25 days
  4. 7.5 days
  5. None of these

Ans: 3.33 days

Solution: Ash can do a job in 10 days,

So efficiency of Ash = 100/10 = 10%

Similarly, Bali’s efficiency = 100/5 = 20%

Combined efficiency of Ash + Bali per day becomes = 20 + 10 = 30%

Now, we have to find out the number of days taken by both Ash and Bali to do 100% work,

Since they can do 30% wok in 1 day,

So, they will 100% work in 100/30 = 3.33 days

NOTE: Efficiencies get added directly!

 Q2: A can do a work in 6 days and B can do the same work in 5 days. The contract for the work is Rs 220. How much shall B get if both of them work together?

Shortcut trick : As wages distributed in inverse proportion of number of days, their share should be in the ratio 5:6

B’s share = 220/11 * 6 = 120

Most of the time and work questions can be solved if you know the basic correlation between time, work and man-hours.

  • Analogy between problems on time and work to time, distance and speed:
    1. Speed is equivalent to rate at which work is done
    2. Distance travelled is equivalent to work done.
    3. Time to travel distance is equivalent to time to do work.
  • Man – Work – Hour Formula:
    1. More men can do more work.
    2. More work means more time required to do work.
    3. More men can do more work in less time.
    4. MM men can do a piece of work in TT hours, then Total effort or work =MT man hoursTotal effort or work =MT man hours.
    5. Rate of work * Time = Work DoneRate of work * Time = Work Done
    6. If AA can do a piece of work in DD days, then AA’s 1 day’s work = 1D1D.
      Part of work done by AA for tt days = tDtD.
    7. If AA’s 1 day’s work = 1D1D, then AA can finish the work in DD days.
    8. MDHW=ConstantMDHW=Constant
      Where,

M = Number of men
D = Number of days
H = Number of hours per day
W = Amount of work

    1. If M1M1 men can do W1W1 work in D1D1 days working H1H1 hours per day and M2M2 men can do W2W2work in D2D2 days working H2H2 hours per day, then

M1D1H1W1=M2D2H2W2M1D1H1W1=M2D2H2W2

    1. If AA is xx times as good a workman as BB, then:
      • Ratio of work done by AA and BB = x:1x:1
      • Ratio of times taken by AA and BB to finish a work = 1:x1:x ie; AA will take (1x)th(1x)th of the time taken by BB to do the same work.

Shortcuts for frequently asked time and work problems

  • AA and BB can do a piece of work in ‘a’′a′ days and ‘b’′b′ days respectively, then working together:
    1. They will complete the work in aba+baba+b days
    2. In one day, they will finish (a+bab)th(a+bab)th part of work.
  • If AA can do a piece of work in aa days, BB can do in bb days and CC can do in cc days then,

A, B and C together can finish the same work inabcab+bc+ca daysA, B and C together can finish the same work inabcab+bc+ca days

  • If AA can do a work in xx days and AA and BB together can do the same work in yy days then,

Number of days required to complete the work if B works alone=xyx−ydaysNumber of days required to complete the work if B works alone=xyx-ydays

  • If AA and BB together can do a piece of work in xx days, BB and CC together can do it in yy days and CCand AA together can do it in zz days, then number of days required to do the same work:
    1. If A, B, and C working together = 2xyzxy+yz+zx2xyzxy+yz+zx
    2. If A working alone = 2xyzxy+yz−zx2xyzxy+yz-zx
    3. If B working alone = 2xyz−xy+yz+zx2xyz-xy+yz+zx
    4. If C working alone = 2xyzxy−yz+zx2xyzxy-yz+zx
  • If AA and BB can together complete a job in xx days.
    If AA alone does the work and takes aa days more than AA and BB working together.
    If BB alone does the work and takes bb days more than AA and BB working together.

Then,x=ab−−√ daysx=ab days

  • If m1m1 men or b1b1 boys can complete a work in DD days, then m2m2 men and b2b2 boys can complete the same work in Dm1b1m2b1+m1b2Dm1b1m2b1+m1b2 days.
  • If mm men or ww women or bb boys can do work in DD days, then 1 man, 1 woman and 1 boy together can together do the same work in Dmwbmw+wb+bmDmwbmw+wb+bm days
  • If the number of men to do a job is changed in the ratio a:ba:b, then the time required to do the work will be changed in the inverse ratio. ie; b:ab:a
  • If people work for same number of days, ratio in which the total money earned has to be shared is the ratio of work done per day by each one of them.
    AA, BB, CC can do a piece of work in xx, yy, zz days respectively. The ratio in which the amount earned should be shared is 1x:1y:1z=yz:zx:xy1x:1y:1z=yz:zx:xy
  • If people work for different number of days, ratio in which the total money earned has to be shared is the ratio of work done by each one of them.

Special cases of time and work problems

  • Given a number of people work together/alone for different time periods to complete a work, for eg: AA and BB work together for few days, then CC joins them, after few days BB leaves the job. To solve such problems, following procedure can be adopted.
    1. Let the entire job be completed in DD days.
    2. Let sum of parts of the work completed by each person = 1.
    3. Find out part of work done by each person with respect to DD. This can be easily found out if you calculate how many days each person worked with respect to DD.
    4. Substitute values found out in Step 3 in Step 2 and solve the equation to get unknowns.
  • A certain no of men can do the work in DD days. If there were mm more men, the work can be done in dd days less. How many men were there initially?

Let the initial number of men be MM
Number of man days to complete work = MDMD
If there are M+mM+m men, days taken = D−dD-d
So, man days = (M+m)(D−d)(M+m)(D-d)
ie; MD=(M+m)(D−d)MD=(M+m)(D-d)
M(D–(D−d))=m(D−d)M(D–(D-d))=m(D-d)

M=m(D−d)dM=m(D-d)d

  • A certain no of men can do the work in DD days. If there were mm less men, the work can be done in dddays more. How many men were initially?

Let the initial number of men be MM
Number of man days to complete work = MDMD
If there are M−mM-m men, days taken = D+dD+d
So, man days = (M−m)(D+d)(M-m)(D+d)
ie; MD=(M−m)(D+d)MD=(M-m)(D+d)
M(D+d–D)=m(D+d)M(D+d–D)=m(D+d)

M=m(D+d)dM=m(D+d)d

  • Given AA takes aa days to do work. BB takes bb days to do the same work. Now AA and BB started the work together and nn days before the completion of work AA leaves the job. Find the total number of days taken to complete work?

Let DD be the total number of days to complete work.
AA and BB work together for D−nD-n days.
So, (D−n)(1a+1b)+n(1b)=1(D-n)(1a+1b)+n(1b)=1
D(1a+1b)–na−nb+nb=1D(1a+1b)–na-nb+nb=1
D(1a+1b)=n+aaD(1a+1b)=n+aa

D=b(n+a)a+bD=b(n+a)a+b days.

Frequently asked questions in quantitative aptitude test on time and work

  • Given A takes x days to do work. B takes y days to do the same work. If A and B work together, how many days will it take to complete the work.
  • If A and B together can do a piece of work in x days, B and C together can do it in y days and C and A together can do it in z days, find how many days it takes for each of them to complete the work if they worked individually. How many days will it take to complete the work if they worked together?
  • Give A is n times efficient than B. Also A takes n days less than B to complete the work. How many days will it take to complete the work if they worked together?
  • Given A takes x days to do work. B takes y days to do the same work. Now A & B together begins a work. After few days one of them leaves. Also given the other takes n more days to complete the work.
    1. Find total number of days to complete the work.
    2. How many days did they work together?
  • Given A takes x days to do work. B takes y days to do the same work. A started the work and B joined him after n days.
    1. How long did it take to complete the work?
    2. How many days did they work together? Or How long did B work?
  • Case 5 with 3 people joining work one after the other.
  • Given A takes x days to do work. B takes y days to do the same work. If A and B works on alternate days ie A alone works on first day, B alone works on next day and this cycle continues, in how many days will the work be finished
  • Given A alone can complete a job in x days and also B is b% efficient than A. How many days will it take to complete work if B works alone.
  • Problems where combinations of workers [men, women, girls and boys] take some days to do a work. These problems are solved using man days concept.
    1. You have to calculate for another combination of them to complete the work.
    2. How long will one set of people take to complete the entire work?
    3. A certain combination starts the job and after few days leaves the work. Find the number of people from the category who are required to finish the remaining work.
  • Problems related to wages from work. How much each person earns from the work done.

 

Practice Problems On Time and Work

Q1: A, B and C can do a work in 6, 8 and 12 days respectively. Doing that work together they get an amount of Rs. 1350. What is the share of B in that amount?

Shortcut trick: A’s share : B’s share : C’s share =

B’s time * C’s time : A’s time * C’s time : A’s time * B’s time

= 96 : 72 : 48 = 4 : 3 : 2

B’s share = 1350/9 * 3

= 450 Rs.

Q2: A is 20% more efficient than B and 50% more efficient than C. if they together can do a work in 24 days then find in how many days B alone can do the work?
A) 60days
B) 72days
C) 90days
D) 180days
E) 100days

View Answer : Option B
Solution: 

.                  A ………B   |   A………C
Efficiency    6……….5    |   3………2
Days            5……….6   |   2………3
Days A : B : C
.        10 12 15
A = 10……….6
B = 12………..5 ….        (LCM = 60)
C = 15………..4
A+B+ C = 15
60/15=4
4=24
1= 6
B=12= 12*6 = 72days

Q3: A can a work in 50 days and B is 50% efficient than A. find in how many days A and B together can complete the work?
A) 30
B) 40
C) 50
D) 33(1/3)
E) 16(2/3)

View Answer : Option D
Solution: 
B is 50% efficient than A

.                   A………..B
Efficiency    2……….. 1
Days            1…………2
1 == 50  . So 2 == 100
A= 50……….2               (LCM = 100)
B =100………1
A+ B = 3
100/3 =33(1/3) days.

Q4: 30 men are supposed to do a work in 38 days. After 25 days, 5 more men were employed on work for which the work is completed in 1 day before . If 5 more men were not worked then how many days took in delay?
A) 1 day

B) 2 days
C) 3 days
D) 4 days
E) None of these.

View Answer : Option A
Solution:  30Men * 25 days = 750
35 Men * 12 Days = 420
Total =750+420=1170
Now,1170/30 =39 days
1 day delay

Q5: A group of men decided to do a job in 4 days but 20 men dropped out everyday ,the job was completed at the end of the 7th day .Find the men who are in the work initially ?
A) 155
B) 135
C) 120
D) 140
E)  160

View Answer :  Option D
Solution:
Total work = M * 4 = 4M
M + (M+20) +…….
7/2 [2M +6(-20)] =4M
M=140

Q6: Ram and Ritesh can do a piece of work in 24 and 30 days respectively. They both started and worked for 6 days. Ritesh then leaves the work and another their friend Ronie joins the work and completed the remaining work with Ram in 11 days . Find how many days are taken by Ronie alone to finish the work?
A) 110 days

B) 132 days
C) 150 days
D) 120 days
E) None of these.

View Answer : Option D
Solution:
(1/24 + 1/30) *6 +(1/24 + 1/Ronie ) *11 = 1
Therefore ,Ronie takes 120 days to finish the work.

Q7: A tap take 42hrs extra to fill a tank due to a leakage equivalent to half of its inflow. The inlet pipe alone can fill the tank in how many hour?
A) 42hrs
B) 21hrs
C) 36hrs
D) 28hrs
E) 30hrs

View Answer : Option A
Solution:

.Without leak……………………With leak
Efficiency   2………………………….1
Time         1…………………………..2
.                   +1 == 42hours
So 42hours

Q8: A can write 75 pages in 25 hrs. A and B together can write 135 pages in 27 hrs.  In what time can B write 42 pages?
A) 17
B) 19
C) 23
D) 21
E) 20

View Answer : Option D
Solution:

A can write 75/25 =3pages in 1hr
A+B can  135/27 = 5pages in 1hr
B can write 5-3 = 2page in 1hr
42/2 =21hrs

Q9: A & B can do a piece of work in 80days. B & C can do same work in 50 days and C & A can do same work in 60 days. Find in how many days they all together can complete that work?
A) 40 (40/59)
B) 60 (40/59)
C) 36 (40/59)
D) 25 (40/59)
E) 26 (40/59)

View Answer : Option A
Solution:

LCM = 2400
A + B = 80………….2400/80 = 30
B + C = 50…………………………..48
C + A = 60…………………………..40
2(A + B + C) = 118
A+ B + C = 59
So 2400/59  days

Q10: A & B separately can do a piece of work in 9days and 12days respectively. If they work for a day alternatively, A starts the work, in how many days will the work will get completed?
A) 12(1/4)

B) 10(1/4)
C) 8(1/6)
D) 10(5/6)
E) 9(1/6)

View Answer : Option B
Solution:

A=9        4
B=12      3          [LCM=36]
2 days alternate            (4+3) = 7 days
2*5            7*5
10days       35days
now A’s turn so-  10(1/4) days

Q11: A and B together can complete a work in 30days and B alone can do it in 60days. Find in how many days A alone can do the work?
A) 40
B) 60
C) 120
D) 90
E) 110

View Answer  Option B
Solution:

A+B…30……2
B……60……1……………(LCM=60)
A  ……………1
A = 60/1 = 60

 

 

 

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