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.

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

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

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

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

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

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

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

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

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

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

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?