1. Time and Work
When we have to compare the work of several persons, it is necessary to
ascertain the amount of work each person can complete in one day.
As time and work are of inverse variation and if more people are joined
to do a work, the work will be completed within a shorter time.

2. In solving problems here, the following points should be remembered:
1. If a man finishes total work in ‘n’ days, then in one day he does
of the total work. For example, if a man finishes a work in 4 days, then in
one day he does
2. If the quantity of work done by a man in one day is given, then the
total number of days taken to finish the work = 1/(one day’s work). For
example, if a man does
taken to finish the work
of the work.
of the work in 1 day, then the number of days

3. Example 1:- A can do a piece of work in 20 days and B can do it in 30 days. How long will they take to do the work together?
Solution
Given:-A do work in 20 days; B does in 30 days.
To Find:- How long both takes if work altogether is done?
Work done by A in one day
Work done by B in one day
Total number of days required to finish the work by A and B
Ans:- They need to work together for 12 days

4. Example2 : A and B together can do a piece of work in 8 days, but A alone can
do it in 12 days. How many days would B alone take to do the same work?
Solution
Given:- A and B takes 8 days, but A alone takes 12 days,
To Find:- How many days B takes?
Work done by A and B together in 1 day
Work done by A in 1 day
Work done by B in 1 day
Number of days taken by B alone to do the same work
Ans:- B alone will take 24 days to finish the work

5. Example 3:- Two persons A and B are engaged in a work
Example 3:- Two persons A and B are engaged in a work. A can do a piece of
work in 12 days and B can do the same work in 20 days. They work together
for 3 days and then A goes away. In how many days will B finish the work?
Solution:-
Work done by A in 1 day
Work done by A and B together in 1 day
, Work done by B in 1 day
Work done by A and B together in 3 days

6. Remaining Work
Number of days taken by B to finish the remaining work
= 3 x 4 =12
Ans:- B will finish the work in 12days

7. Example 4:- A and B can do a piece of work in 12 days, B and C in 15 days, C and A
in 20 days. In how many days will they finish it together and separately?
Solution:-
Work done by A and B in 1 day
Work done by C and A in 1 day
Work done by (A+B)+(B+C)+(C+A) in 1 day
Work done by (2A + 2B + 2C) in 1 day
Work done by 2(A + B + C) in 1 day
Work done by A, B and C together in 1 day
∴ A,B and C will finish the work in 10 days.
,Work done by B and C in 1 day

8. Work done by A in 1 day
i.e [(A + B + C)’s work – (B + C)’s work
∴ A will finish the work in 30 days.
Work done by B in 1 day
(i.e.) [(A + B + C)’s work – (C + A)’s work]
∴ B will finish the work in 20 days.
Work done by C in 1 day
i.e.,[(A + B + C)’s work – (A + B)’s work]
∴ C will finish the work in 60 days

9. Example 5:- A can do a piece of work in 10 days and B can do it in 15 days. How
much does each of them get if they finish the work and earn Rs. 1500?
Solution:-
Work done by A in 1 day
Ratio of their work
Total Share = Rs. 1500
, Work done by B in 1 day
= Rs.900
= Rs.600
Ans:- A get Rs 900 and B gets Rs 600

10. Example 6:- Two taps can fill a tank in 30 minutes and 40 minutes
Example 6:- Two taps can fill a tank in 30 minutes and 40 minutes. Another tap
can empty it in 24 minutes. If the tank is empty and all the three taps are kept
open, in how much time the tank will be filled?
Solution:-
Quantity of water filled by the first tap in one minute
Quantity of water filled by the second tap in one minute
Quantity of water emptied by the third tap in one minute

11. Quantity of water filled in one minute,
When all the 3 taps are opened
Time taken to fill the tank
= 1 hour
Ans:- It will take 1 hour for all 3 taps to fill the tank

12. Try these
A tap A can fill a drum in 10 minutes. A second tap B can fill in 20 minutes.
A third tap C can empty in 15 minutes. If initially the drum is empty, find
when it will be full if all taps are opened together?