Time and Work Solved Examples
Solved examples on Time and Work:
Question: Mohan can do a piece of work in 10 days and Ramesh can do same work in 15 days. How long will they take if both work together?
(10*15)/(10+15) =6 days
Question: A and B together can complete a piece of work in 4 days, If A alone can complete the same Work in 12 days, in how many days can B alone complete that work?
Question: A and B can do a piece of work in 18 days; B and C can do it in 24 days; A and C can do it in 36 days. In how many days will A, B and C ﬁnish it. Working together and separately?
Twice of work done by A, B and C
(72 being lcm of 18,24,36)
So A B and C together can do that work in 16 days.
Time taken by A = (24*16)/(24-16)=48 days
Time taken by B = (36*16)/(36-16)= 144/5 days=28 4/5 days
Time taken by C = (18*16)/(18-16)= 144 days
Question: A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A beginning, in how many days, the work will be completed?
A+B ‘s 2-day work = 7/36
10 days (5 pairs) of combined work =35/36
Work left=1/36 which is to be done by A in 1/36 divided by 1/9 i.e. 1/4 days
Hence, total time taken is 10 ¼ days
Question: A can do a certain job in 12 days.B is 60% more efficient than A. How many days does B alone take to do the same job?
B will do the same work in (12*100)/160= 7.5 days
Question: 45 men can complete a work in 16 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?
After six days:
Question: A is twice as good a workman as B and together they ﬁnish a piece of work in 18 days. The number of days taken by A alone to ﬁnish the work is:
3B works in 18 days so B will do the same in (18*3)=54 days
hence A will do it in 54/2=27 days
Together they will take 42/(1+2)=14 days
Question: A and B can Complete a work in 15 days and 10 days respectively. They 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:
A and B can complete whole work in
Part of work completed together in
3 days =2/6=1/3 part
Now 2/3 part will be completed by A in
Hence, whole work will be completed in
Question: A and B can together ﬁnish a work in 30 days. They worked together for 20 days and then B left. After another 20 days, A ﬁnished the remaining work. In how many days A alone can finish the job?
In 20 days, 2/3 part of work is done and 1/3 part is left
And A finishes 1/3 part in 20 days,
hence whole work can be done by A in 60 days
Question: A, B and C can complete a work separately in 24, 36 and 48 days respectively. They started together, but C left after 4 days of start and A left 3 days before the completion of the work. In how many days will the work be completed?
Let the work be completed in X days
(X-3)/24 + X/36 + 4/36 = 1
Solving the Eqn. X= 15
Hence, work will be completed in 15 Days
Question: If 12 men and 16 boys can do a piece of work in 5 days and 13 men and 24 boys can do it in 4 days, how long will 7 men and 10 boys take to do it ?
5(12m+16b) = 4 (13m+24b)
From part one, 40 (24+16 ) boys can do it for 5days
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