This is the aptitude questions and answers section on 'Time and Work' with solutions and detailed explanation. Questions on time and work deal with the simultaneous performance involving efficiency of an individual or a group and the time taken by them to complete a piece of work.
Problems on Time and Work : Question 1 :
A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in how many days?
(A + B)’s one day’s work = 1/10. --- (i)
C’s one day’s work = 1/50
(A + B + C)’s one day’s work = (1/10 + 1/50) = 6/50 = 3/25. ---- (ii).
Also, A’s one day’s work = (B + C)’s one day’s work.
From (i) and (ii), we get :2*(A’s one day’s work) = 3/25.
=> A’s one day’s work = 3/50
B’s one day’s work = (1/10 - 3/50)
Thus, B alone could complete the work in 25 days.
Problems on Time and Work : Question 2 :
Pipe A and B can fill a tank in 8 hours, B and C can fill it in 12 hours. A, B and C together can fill it in 6 days. A and C together will fill it in how many days?
Let the total units of work be 48.
Units of work completed by A and B in one day = 6.
Units of work completed by B and C in one day = 4
Units of work completed by A, B, and C in one day = 8.
From the above information we get the work completed by A and C in one day is 6 units.
Therefore, the number of days taken by A and C to complete the whole work = 48/6 = 8 days.
Problems on Time and Work : Question 3 :
Ajay can complete a piece of work in 4 days. Balu takes double the time taken by Ajay, Charan takes double that of Balu, and Danush takes double that of Charan to complete the same task. They are paired in groups of two each. One pair takes two thirds the time needed by the second pair-to complete the work. Which is the first pair?
Time taken by Ajay, Balu, Charan, Dhanush is 4 days, 8 days, 16 days and 32 days respectively.
Therefore, grouping Ajay and Dhanush work will be two third of the work that will be completed by grouping Balu and Charan.
Problems on Time and Work : Question 4 :
5 persons working eight hours daily can complete a wall in 10 days. When they have Worked for 4 days, 5 more persons are brought to work. The wall can now be completed in?
Let D be the number of required days
Using the chain rule,
M1 x T1 = M2 x T2 + M3 x T3
5 x 8 x 10 = (4 x 5 x 8) + (10 x 8 x D)
D = 3.
Hence, the wall will be completed in 3 more days.
Problems on Time and Work : Question 5 :
24 men working at 8 hours a day can finish a work in 10 days. Working at the rate of 10 hours a day, the number of men required to finish the same work in 6 days is?
Using Using the chain rule,
M1 x T1 = M2 x T2
Therefore, 24 x 8 x 10 = 10 x X x 6
Hence, the number of men required to finish the work = 32.