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?

Solution:

(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?

Solution:

(12*4)/(12-4)= 6 days

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?

Solution:

Twice of work done by A, B and C

together=72/(4+3+2)=8 days

(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?

Solution:

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?

Solution:

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?

Solution:

After six days:

45*10=75*x

X=6 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:

Solution:

A=2B (work)

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:

Solution:

A and B can complete whole work in

30/(2+3)=6 days

Part of work completed together in

3 days =2/6=1/3 part

Now 2/3 part will be completed by A in

2/3*15=10 days

Hence, whole work will be completed in

2+10=12 days

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?

Solution:

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?

Solution:

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 ?

Solution:

5(12m+16b) = 4 (13m+24b)

1m=2b

From part one, 40 (24+16 ) boys can do it for 5days

Hence 24 (14+10) boys can do it for 25/3 days.

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