Practice Time And Work Problems with short tricks Practice Time And Work Problems With Short Tricks

Q1. Worker A takes 8 hours to do a job,worker B takes 10 hours to do the same job.Find the total time taken by A and B both working together?

Solution:

A’s 1 day work=(1/8)
B’s 1 day work=(1/10)
When they(both) do that work, their 1 day work=(1/8 + 1/10)= 9/40
Total time = 40/9 days(reversing fraction of 1 day work gives total time)

Short trick

Take L.C.M of 8,10 = 40
Let 40 unit of work is there.
A does 5 unit and B does 4 unit .So,both will do 9 unit of work.
Total time taken to do 40 unit = 40/9 ans

Q2.A and B can do a piece of work in 4 days working together.A alone do the same work in 12 days.Find the time taken by B to complete the same work? Ans-6 days

Solution:

A+B’s 1 day work=(1/4)
A’s 1 day work=(1/12)
B’s 1 day work=(1/4 – 1/12)= 1/6
Total time = 6 days(reversing fraction of 1 day work gives total time)

Short trick

Take L.C.M of 4,12 = 12
Let 12 unit of work is there.
A does 1 unit and A+B(both) does 3 unit .So,B will do (3-1)=2 unit of work.
Total time taken to do 12 unit = 6days ans

Q3.A and B paints a house in 18 days,B and C paint the same house in 24 days,A and C paints it in 36 days.Find the time taken by A,B,C when they alone paints the house.Also find the time taken when they start painting house together? Ans-(A-48 days,B-144/5 days,C-144,(A+B+C)-16 days

Solution:

A+B’s 1 day work=(1/18)——(1)
B+C’s 1 day work=(1/24)——(2)
A+c’s 1 day work=(1/36)——(3)
2(A+B+C)’s 1 day work= 9/72 = 1/8
(A+B+C) 1 day work= 1/16——(4)
total time taken by A,B,C=16 days
When we subtract eqn (1) from (4), we get C’s 1 day work = (1/16 – 1/18)= 2/288 = 1/144
Total time taken by C = 144 days
Similarly For B = 144/5 days
Similarly For A = 48 days

Q4.A is twice as good workman as B and together they finish the work in 18 days.Find the time taken by A to complete the work? Ans-27 days

Solution:

A is twice as good workman as B.It means A takes less time than B.Ratio of time taken i.e A:B=1:2
Let A does in k days then B will do in 2k days
A+B ‘s 1 day work = (1/k + 1/2k)=3/2k
And, (3/2k)=(1/18)
so, k=27
A will complete in 27 days.

Short trick

Take L.C.M of 4,12 = 12
If A is twice as good as workman B.It means if A does 2 unit of work B will do 1 unit work in 1 day.
both will do (2+1) = 3 units.
So, in 18 days total work= 18*3=54 unit
A will do the whole work in (54/2)=27 day
And B will do in 54 days.

Q4.Ramesh builds a motor bike in 80 days.He starts building the motor bike and leaves it after 10 days.Rohan works on the same bike and completes building it in 42 days.Find the time in which Rohan alone can build that motor bike? Ans-30 days

Solution:

A+B’s 1 day work=(1/4)
A’s 1 day work=(1/12)
B’s 1 day work=(1/4 – 1/12)= 1/6
Total time = 6 days(reversing fraction of 1 day work gives total time)

Short trick

Take L.C.M of 4,12 = 12
Let 12 unit of work is there.
A does 1 unit and A+B(both) does 3 unit .So,B will do (3-1)=2 unit of work.
Total time taken to do 12 unit = 6days ans

Practice Rest of Time And Work Problems with yourself

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Q5.A and B undertake to do a piece of work for Rs 600.A alone can do it in 6 days and B can do it in 8 days.With the help of C they do the work in 3 days.Find their Share? Ans-(A-300,B-225,C-75)

Q6.A is 30%more efficient than B.What will be the time taken to complete that job which A alone can do it in 23 days? Ans -13 days

Q7.10 women can complete the work in 7 days whereas 10 children can complete the work in 14 days.Find the time taken by 5 women and 10 children to do the job? Ans-7 days

Q8.A alone can do a work in 16 days and B can do it in 12 days.Starting with A ,they work on alternate days.Find the total time taken to complete the work? Ans-55/4 days

Q9.If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same work in 2 days. In how many days 15 men and 20 boys can do the same work? Ans-4 days

Q10.A can do a piece of work in 40 days.A works for 8 days and B do it in 16 days.How long will they take to finish the work working together? Ans-40/3 days

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