Time and Work Questions With Solutions
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| Time and Work Questions |
Introduction
In this tutorial we see all the important questions time and work also we see all the basic formulas.
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In any industries there should be a aptitude round and it is very important to crack the round to further process.
So, for this aptitude preparation we cover all the mathematical questions with answers.
time and work questions with solutions
So,in this tutorial we see the time and work topic important questions with solutions.
Important Facts and Formulae
1.To calculate capacity
Capacity = Work/Time
2.To calculate work
Work = (Rate of work) ✖ (Time)
3.To calculate work done by both(Together) A and B
(Â Â 1 / (1/A+1/B)Â )
4.If A person can complete a piece of work in 'n' days thenÂ
A's 1 Days work = 1/n
5.A's 1 Days work = 1/n
Then A can finish there work in n daysÂ
NOTE
In short if we want calculter the XYZ person 3 day work then the formula is 1/3
So, here we can say that XYZ person required to complete his work for 3 days.
6. If A is work thrice more than B then
Ratio of work done by A and B=3:1
So,Here to calculate the ratio of time taken by A and B to complete his work = 1 : 3
7. To calculate efficiency use following formula
Efficiency = (1/Time taken to complete a task)
8. To calculate work doneÂ
Work done=(Number of workers)×
           ( Efficiency ) ×(Time)Â
Important examples with solution to crack the aptitude all questions from year 2003 to 2023Â
1.Worker a takes 8 hours to do a job.worker B takes 10 hours to do the same job. How long it taken both A and B, Working together but independently,to do the same job?(Time and Work Questions)
 →
 A,s 1 hour work = 1/8
                   Â
 B,s 1 hour work = 1/10
(A and B )'s 1 hour's workÂ
Here we simplify  Â
 =   (1/8 + 1/10) Â
=Â Â 10 + 8Â / 80Â
=Â Â 18 / 80Â Â
=Â Â 9/40
                                    Â
Ans.  Both A and B complete his work in 40/9 = 4 (4/9)
2.A and B together can complete a piece of work in 4 days.If A alone can complete the same work in 12Â days ,in how many days can B alone complete that work?
→
First we calculate the A and B 1 day work together
(A+B) 1 day's work =1/4
Now, we calculate A work alone same work in 12 days
So, here A's 1 day's work = 1/12
Now we calculate the how many days B required to complete same workÂ
∴ B's 1 day's work = [( 1/4)-(1/12)]
                 Â
 Ans.  So,B alone complete that work in 1/6 days
3. A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they take to do it, working together 8 (2/5)
→
First we calculate A's work hours
A can complete the work in
(7×9) = 63 hours              Â
Then we calculate B's work hours
B can complete the work inÂ
(6×7) = 42 hours
               Â
Now we calculate A's and B's 1 hour work.
∴ A's 1 hour's work = 1/63
  B's 1 hour's work = 1/42
Now,here we calculate the together 1 hour's work of A and B
∴ (A + B) 1 hours workÂ
=Â [(1/63)+ (1/42)]Â
= 5/126
                       Â
So here both will finish the work in (126/5) hours
Now, calculate the how long they take to do it means calculate the days for 8(2/5)
∴ Number of days 8(2/5) hrs eachÂ
=(126/5 × 5/52)
Ans.   Number of days 8(2/5) hrs each is 3 days
               Â
4. A is twice as good a workman as B and together they finish a piece of work in 18 days.In how many days will A alone finish the work?
→
Here we find out work ratio of A and B
(A's1 days work ):( B's 1 days work)
             2 : 1
(A + B)'s 1 day's work = 1/18
Divide 1/18 in the 2:1 ratioÂ
∴ A's 1 days workÂ
= {(1/18)×(2/3)}
                Â
= 1/27
Ans.   Hence, A alone can finish the work in 27 days.
5.Mahesh can do a certain job in 12 day's and sanket is 60% more efficient than mahesh.How many days does sanket alone take to do the same job?
→
Here, we first calculate the ratio of mahesh and sanket jobs
Ratio of time taken by mahesh and sanket Â
=Â 160 : 100
       Â
=Â Â 8Â Â Â :Â Â 5
Suppose sanket alone takes x days to do the job
8 :5: :12 : xÂ
∴ 8x = 5×12Â
                Â
 Ans.  x =7(1/2) day's
       Â
6. A does a work in 10 days and B does the same work in 15 days.In how many days they together will do same work?
→
First we find out the A's 1 day work = 1/10
B's 1 day's work = 1/15
∴ Then we fine there together work
( A+ B ) both 1 day workÂ
= {(Â 1/10)+(1/15)}
Ans.  There together work is 1/6
7. A can finish a work in 18 days and B can do the same work in half the same time taken by A Then, working together what part of the same work they can finish in a day?
→
A's 1 day's work = 1/18
B's 1 day's work = 1/9
∴ ( A+ B ) both 1 day workÂ
= {(Â 1/18)+(1/9)}
Ans- ( A+ B ) both 1 day work is 1/6
8.A,B, and C can complete a piece of work in 24 ,6,12 days respectively . Working together they will complete the same work inÂ
→
Here we calculate the A,B,C together 1 day's work
∴ (A+B+C) 1 day's workÂ
= {(1/24+1/6+1/12)}
=7/24
Ans.  So A,B,C together will complete the work in 24/7 days.
9.A man can do a piece of work in 5 days,but with the help of his son ,he can do it in 3 days .In what time can the son do it alone?
→
Here we calculate the son alone 1 day work hence here we minus the sons work from A man work
So,here sons work is 1/3
A's work is 1/5
Now we calculate the sons alone work
Son 1 days workÂ
={(1/3)-(1/5)}
=2/15
Ans.     The son alone can do the work in 15/2 days.
10.A takes as twice as much time as B or thrice as much time to finish a piece of work.Working together,they can finish work in 2 days.B can do the work alone in how many days. Â
→Â
Here we just suppose A,B,C which takes
A = X
B=X/2
C=X/3 Hours respectively to finish a piece of work
So,we want find the in how many days B can do the work aloneÂ
∴ {(1/x+2/x+3/x)}=1/2
Working together,they can finish work in 2 days hence as per mention in question here we take 1/2
6/x=1/2
x=12
Ans.   B can do the work alone in 12 days
11. A and B can finish the work in 12 days,B and C in 15 days and C and A in 20 days so if they are complete the work together that means both A,B and C in how many days they complete the same work?Â
→Â
Here we find out the A+B, B+C, A+C 1 days work
∴ A+B 1 days work
=1/12
B+C 1 days work
=1/15
A+C 1 days work
=1/20
Now, we find out the together there workÂ
Adding we get,
2(A + B + C) 1 days work
= 2{(1/12 +Â 1/15 +Â 1/20)}
= 2 (12/60)
=2(1/5)
=10
Ans.  A + B + C 1 days work is 10 days
12.A complete a work in 15 days and B can complete a work in 10 days.They both started doing the work together but after 2 days B had to leave and A alone completed the remaining work.The whole work was completed in how many days?
→
( A+B) 1 Days work together is
= (1/15 + 1/10)
= 1/6.
Now,we calculate work done by A and B in 2 daysÂ
= (1/6×2)
= 1/3
Now we have to calculate the remaining workÂ
= (1-1/3)
=2/3
Now we see that,
A 1 days work is 1/15
∴ Remaining work that is 2/3 is done by A inÂ
= (15 × 2/3)
=10 daysÂ
Ans.  Whole work was completed = 10 + 2=12 days.
Problems for Practice
1.A man can do a job in 15 days.His father takes 20 days and his son finish it in 25 days .How long will they take to complete the job by together?
Options
1) less than 6 days
2) Exactly 6 days
3) Approximately 6.4 daysÂ
4) More than 10 days
Answer.  Option 3
2.A and B can do piece of work in 8 days ,B and C in 12 days same work do and A,B,C together can finish in 6 days so A and C can do it in how many days?
Options
1) 4 days
2) 6 days
3) 8 days
4) 12 days
Answer.  Option 3
3.A and B complete a piece of work in 72 days ,Same work done by B and C in 120 days and A and C can finish it in 90 days .In what time A can alone do it?
Options
1) 80 days
2) 100 days
3) 120 days
4) 150 days
Answer.  Option 3
4. A can do work in 4 hours as B and C do it together in 3 hours and A and C do it in 2 hours. how long will B alone take to do it?
Options
1) 8 hours
2)10 hours
3) 12 hours
4) 24 hours
Answer. Option 3
5.A work twice as faster as compared to B.If B can finish there work alone in 12 days the number of days in which A and B can complete the work?
Options
1) 4 days
2) 6 days
3) 8 days
4) 18 days
Answer.  Option 1
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6.A is twice as good as compared to B and together they can finish a piece of work in 14 days the number of days taken by A to finish the work?
Options
1) 11 days
2) 21 days
3) 28 days
4) 42 days
Answer. Option 2
7.A can finish a work in 18 days B can complete the same work in 15 days .B worked for 10 days and then left the job.In how many days A can finish independent the remaining work?
Options
1) 5 days
2) 5(1/2)days
3) 6 days
4) 8 days
Answer.  Option 3
8.Abhi and sumit can complete a work in 15 days and 10 days respectively.They started doing the work together but after 2 days sumit had to leave and abhi alone completed the remaining work.how many days required to complete the work.
Options
1) 8 days
2)10 days
3) 12 days
4) 15 days
Answer.  Option 3
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