TIME AND WORK
Time and Work
• Introduction
• Relationship b/w Time, Work & Efficiency
• LCM approach
• Partial work done problems
• Problems related to efficiency
• Work done on alternate days
• Negative work
• DI and DS on Time and work
Remainders
Time and Work
TIME AND WORK CONCEPT
A certain amount of time (T) is taken to complete a certain work (W).
The number of units of work done per unit time is called the efficiency of work (E).
Hence, Work (W) = Efficiency (E) x Time (T)
Remainders
Time and Work
Formulas Including Short Tricks
1. If M1 persons can do W1 work in D1 days working T1 hours in a day and M2 Persons can do
W2 work in D2 days working T2 hours in a day then the relationship between them is
2. If A can do a piece of work in x days and B can do the same work in y days then (A + B)’s one day
work.
Time taken by (A + B) to complete the work is
3. If ‘n’ persons (more than two) are there then their one day’s work =
here x1,x2, x3 …………… represents the number of days taken by them to complete the work.
Remainders
Time and Work
Formulas Including Short Tricks
4. Universal Rule
This rule can be used in almost every problem.
If M1 persons can do W1 work in D1 days and M2 persons can do
W2 works in D2 days then we can say
M1×D1×W2 = M2×D2×W1
If the persons work T1 and T2 hours per day respectively then the
equation gets modified to
M1×D1×T1×W2 = M2×D2×T2×W1
If the persons has efficiency of E1 and E2 respectively then,
M1×D1×T1×E1×W2 = M2×D2×T2×E2×W1
Remainders
Time and Work
1. A can do 1/2 of a piece of work in 5 days. B can do 3/5 of the same work in 9 days and C
can do 2/3 of the work in 8 days. In how many days can three of them together do the work.
[ Problem based on LCM]
A. 4 days B. 5 days C. 10 days D. 12 days
Remainders
Time and Work
2. A and B can complete a work in 9 days and B and C can complete the same work in 15
days. If B alone can complete the work in 45 days, in how many days A and C can complete
the work? [ Problem based on LCM]
A. 4 days B. 3 days C. 4.5 days D. 7.5 days
Time and Work
3. A and B together can do a piece of work in 30 days. B and C together can do the same work in 45 days
& C and A together complete it in 60 days. In how many days C alone could complete it?
[ Problem based on LCM]
A. 120 days B. 180 days C. 360 days D. 250days
Remainders
Time and Work
4. A can do a piece of work in 15 days. B can do the same work in 25 days. Both together
started the work and after 5 days B left the work. In how many days A complete the
remaining work? [ Problem based on Partial Work Done]
A. 4days B. 5 days C. 7 days D. 12 days
Remainders
Time and Work
5. A can do a piece of work in 20 days. B can do the same work in 30 days. Both together
started the work and B left the work 5 days before the completion. For how many days A
and B together work? [ Problem based on Partial Work Done]
A. 7 days B. 5 days C. 8 days D. 9 days
Remainders
Time and Work
6. Riya and Priya can together finish a work in 30 days. They worked together for 20 days
and then Priya left. After another 20 days, Riya finished the remaining work. In how many
days Riya alone can finish the work? [ Problem based on Partial Work Done]
A. 45 B. 60 C. 35 D. 50
Remainders
Time and Work
7. P can do 3/5th of work in 30 days. Efficiency of Q is 25% more than that of P. Both P and
Q started working together and left the work after 10 days. R completed the remaining work
in 11 days. Efficiency of R is what % more/less than that of Q ? [ Problem based on
Partial Work Done]
A. 20% less B. 100% more C. 20% more D. 25% less
Remainders
Time and Work
8. A can do a work in 16 days. P who is 60 % more efficient than A. Find how much time
they will take together to do the same work? [ Problem based on Efficiency]
A. 150/13 days B. 80/13 days C. 70/13 days D. 90/31 days
Remainders
Time and Work
9. A is twice as efficient as B and thrice as efficient as C. All three together can do a piece
of work in 12 days then find in how many days A and B together could do that work?
[ Problem based on Efficiency]
A. 13.2 days B. 14 days C. 16.33 days D. None
Remainders
Time and Work
10. ‘A’ alone can do half of a work in 70 days. The time taken by B to do 1/4 th of the work
is equal to the time taken by A to do 1/3rd of the work. Find the number of days A and B
together will take to complete the work? [ Problem based on Efficiency]
A. 35 days B. 40 days C. 80 days D. 60 days
Remainders
Time and Work
11. Anamika and Bhumika can do a piece of work in 12 days and 24 days, respectively. As
Anamika was ill, she could do 50% of her efficiency, and Bhumika could do 200% of her
new efficiency. How many days will they take to complete the work together? [ Problem
based on Efficiency]
A. 50/3 days B. 40/3 days C. 6.66 days D. 8 days
Remainders
Time and Work
12. Ram does a work in 40 days and Shyam does same work in 60 days. If efficiency of
Mohan is 20% less than the combined efficiency of Ram and Shyam together then working
alone Mohan will complete the whole work in how many days? [ Problem based on
Efficiency]
A. 20 days B. 25days C. 30 days D. 40days
Remainders
Time and Work
13. B takes 4 times as long as A and C together and C takes thrice as long as A and B
together to complete the work. If A, B and C together complete the work in 30 days, how
long would C alone take to complete the work? [ Problem based on Efficiency]
A. 110 days B. 80 days C. 120 days D. 90 days
Remainders
Time and Work
14. How many days taken by Chitra to finish the work alone. Ashish , Bhavesh and Chitra
working together complete a job in 10days. Ashish and Bhavesh together work twice as
Chitra , Ashish and Chitra together work thrice as much as Bhavesh. [ Problem based on
Efficiency]
A. 30 days B. 25days C. 35 days D. 40days
Remainders
Time and Work
15. A takes three times as long as B and C together to do a job. B takes four times as long as
A and C together to do the same work, If all three, working together can complete the job in
10 days, then the number of days, A alone will take to finish the job is:
[ Problem based on Efficiency]
A. 100 B. 40 C. 95 D. 90 E. None of these
Remainders
Time and Work
16. A can do a piece of work in 12 days , B could do it in 15 days. In how many days work
will be completed if they work in alternate days , starting with A? [ Problem based on
Alternate days]
A. 17.56 days B. 15.25 days C. 13.25 days D. 15 days
Remainders
Time and Work
17. A and B together can complete a piece of work in 15 days but C can destroy the work in
60 days. If B and C work together, then they take 120 days to complete the work. Find the
number of days, A alone will take to complete the work? [ Problem based on Negative
Work ]
A. 24 days B. 42 days C. 60 days D. 48 days
Remainders
Time and Work
18. A can build a wall in 20 days and B can destroy it in 30 days. In how many days wall
will be build if they works in alternate days. Given that A works on the very first day ?
[ Problem based on Negative Work in Alternate days]
A. 110 days B. 115days C. 120 days D. 140days
Remainders
Time and Work
19. X and Z can build a wall in 18 days and 16 days respectively, while Y can destroy the
whole wall in 20 days. If X works with Z on first day, what is the number of days required
to build the wall if X is joined by Y and Z on alternate days? [ Problem based on Negative
Work in Alternate days]
A. 8 11/85 days B. 8 4/85 days C. 16 8/85 days D. 8 13/85 days
Remainders
Time and Work
20. P can do as much work in 4 days as K can do in 6 days, and K can do as much work in 5
days as A in 8 days. What wages does A get for a piece of work which P can do in 80 days,
if A gets Re. 1 for 1 day? [ Problem based on Wages]
A. Rs. 144 B. Rs. 124 C. Rs. 192 D. Rs. 130
Remainders
Time and Work
21. Q can complete a piece of work in 12 days, W can complete the same work in 15 days
and R can complete the work in 20 days. Doing that work together, they get an amount of
Rs.108000. Find the sum of shares of Q and W. [ Problem based on Wages]
A. Rs. 56000 B. Rs. 81000 C. Rs. 42000 D. Rs. 49000
Remainders
Time and Work
22. Rahul and Gaurav completing some work. If Rahul takes 9 days more to
complete a work than the time taken by Gaurav and Rahul together; Gaurav takes 4
days more than the time taken by Rahul and Gaurav together, Then the time taken
by both to finish the work is?
A. 6 B. 12 C. 10 D. 16
Remainders
Time and Work
23. P can finish a work in 10 days. P invites Q and R both of whom individually can work
3/4th as fast as he can, to join him. P also invites S and T both of whom individually can
work 1/5th as fast as he can, to join him. If the five person team works the same job and
they start together, how long will it take for them to finish the job? [Miscellaneous]
A.50/97 days B.87 days C.100/29 days D.50/29 days
Remainders
Time and Work
24. Pratik can do a piece of work in 20 days and Ravi can do it in 12 days. On which date
will they complete the work, if they work together on prime number dates starting on 19th
May?
A.7th June B. 11th june C. 13th june D. 23rd june
Remainders
Time and Work
25. A and B can do a piece of work in 24 days and B and C can do the same piece of work
in 32 days. A work for 10 days and B work for 14 days and C complete the remaining work
in 28 days then in approximate how many days C alone would complete the same work ?
[Miscellaneous]
A. 36 days B. 40 days C. 50 days D. None
Remainders
Time and Work
Direction(26-29)
Study the table chart carefully and give the answer carefully.
26. A and B started the work and they together worked for 10 days then
both left the work and C joined the work and complete the remaining
work. Find for how many days C worked?
A. 3 days B. 4 days
C. 5.5 days D.10days
Remainders
Time and Work
27. D and E together started the work together. After 20 days D left the
Work. In how many days E alone can do the remaining work?
A. 3 days B. 4 days
C. 5 days D. 4.5 days
Remainders
Time and Work
28. In how many days A and E together could do the complete work, if
both works with their half of the efficiency?
A. 30 days B. 40 days
C. 50 days D. 53 days
Remainders
Time and Work
29. If A and C works in alternate days in how many days work will be
completed?
A. 25 days B. 28 days
C. 30 days D. 35 days
Remainders
Time and Work
30. Find in how many days A alone can do the work?
I: If A and B do a work together for 10 days and B left the work and A do the remaining
work in 20 days.
II: B can do the work in 15 days
A) I alone sufficient while II alone not sufficient to answer
B) II alone sufficient while I alone not sufficient to answer
C) Either I or II alone sufficient to answer
D) Both I and II are not sufficient to answer
E) Both I and II are necessary to answer
Remainders
Time and Work
31. A alone can complete a work in 24 days. How many days will A,B,C together take to
complete the work ?.
I. A and B together can complete the work in 6 days.
II. B and C together can complete the work in 12 days.
A) I alone sufficient while II alone not sufficient to answer
B) II alone sufficient while I alone not sufficient to answer
C) Either I or II alone sufficient to answer
D) Both I and II are not sufficient to answer
E) Both I and II are necessary to answer
Remainders
Time and Work
32. A is twice as efficient as B. In how many days both together can complete that work?
I. A can complete the work in 10 days.
II. B can complete the work in 20 days.
A) I alone sufficient while II alone not sufficient to answer
B) II alone sufficient while I alone not sufficient to answer
C) Either I or II alone sufficient to answer
D) Both I and II are not sufficient to answer
E) Both I and II are necessary to answer
Remainders
Time and Work
33. Find in how many days A alone can do the work?
I: If A and B works in alternate days they can complete a work in 10 ¼ days.
II: The ratio of efficiency of A and B is 4:3.
A) Only I
B) Only II
C) Either I or II
D) Neither I nor II
E) Both I and II
Remainders
Time and Work
34. Prashant works for 8 days and leave the job. In how many days Amit can finish the
remining work?
I. Amit can complete the work in 16 days.
II. Prashant and Amit can complete the work in 13 1/3 days.
III. Amit is twice as efficient as Prashant.
A) Only I and III
B) Only I and II
C) Any two of the three.
D) Only II and III.
Any Doubts???
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