Time and Work is an important topic of arithmetic. After going through the basic concepts of this chapter, you would find these questions easy to handle and solve.
1. Three workers, X, Y and Z, do fencing of gardens on contract basis. Y is 25% more efficient than X. If X alone does the work, fencing will take 12 days to complete. A person hires them for fencing for Rs 630 and work is completed in 4 days. Find the amount earned by Z.
2. A team has planned to manufacture 270 units in a scheduled time. For the first three days the team worked as per the plan. Subsequently, the efficiency increased and the team started to manufacture 8 units more than the estimated work plan for a day. This resulted in early completion of the task before two days from the estimated time and also they manufactured 280 units in total. As per the plan, how many units per day should have been manufactured within the scheduled time?
a) 48 units
b) 25 units
c) 30 units
d) 27 units
4. A, B, C alone can construct a house in 15, 30 and 20 days respectively. All together start the work, after 4 days they have some misunderstanding and they start working alternatively starting with A. How many days are required to complete the construction of the house?
a) 12 days
b) 11 days
c) 15 days
d) 17 days
5. An inlet pipe A fill the tank in 15 hour and an outlet pipe B empty the full tank in 20 hour and third inlet pipe C fill the tank at the rate of 50 litre/hour. If all the pipes are opened together, tank will be fill in 10 hour. Find the capacity of the tank?
a) 500 litres
b) 650 litres
c) 600 litres
d) 700 litres
6. Two persons A and B are working on the same project. If B worked alone, he would need 8 days more to complete the project than of they both worked together. Now, if A worked alone, it would need 4.5 days more to complete the project than they both working together. What time would it take A alone to complete the project?
7. If 10 men , 30 women and 40 boys can do a piece of work in 110 days, working for 6 hours each day. In how many days will 20 men , 15 women and 20 boys do another piece of work thrice as large as the first, working 9 hours a day, if the amount of work done by each man, woman and boy is in the ratio 3:2:1?
8. Three workers A, B, C are there to complete a work. A and B work together for 4 hours to complete a single product. C can finish the same product in 10 hours working alone. How many hours will be taken to complete 14 such products if all of them work together?
a) 40 hrs
b) 24 hrs
c) 32 hrs
d) 36 hrs
9. Pipe A can fill a tank in 4 hours. There is a hole at the bottom due to which it takes double time to fill the tank. After filling the tank full, the Pipe A is closed. How long does it take to empty the tank by itself due to leakage?
a) 2 hr 66 min
b) 2 hr 40 min
c) 2 hr 20 min
d) 2 hr 16 min
10. A can finish solving an exercise in 2 hours, B in 3 hours and C in 4 hours respectively. In how many hours will all three complete 100 exercises, considering that no two people work on same exercise?
Explanation (1) : X takes 12 days to complete fencing alone.
Work done by X in 1 day = 1/12
Since Y is 25% more efficient, he will take lesser time for same work
Work done by Y in 1 day = 1/9
As x, y and z together take 4 days to finish the work,
Explanation (2) :
Let the number of units manufactured be X. From the options c and d can be the feasible options. Suppose check for Option C, the work would be complete in 9 days. Then,
3x + 5 (X + 8) = 280, X = 30 units. Hence option (c) is correct.
Explanation (3) : Total man – days needed = 10 X 100 = 1500
Man days worked before 51 day = (50 – 5) X 15 = 675
Man days worked after 51st day = 20 X (46.25 – x), where X is the number of days it rained after day 50.
1500 = 675 + 20 X (46.25 – x)
X = 5 days.
Explanation (4) :
Explanation (5) :
Explanation (6) :
Explanation (7) :
Let the work done be X. Therefore work done by Men : Women: Boys = 3x: 2x:x. No. Of days taken by 20 Men,15 women and 20 boys do another piece of work thrice as large as the first =
Days = 260
Explanation (8) :
Explanation (9) :
Pipe A takes 4 hour to fill the tank.
Part of tank filled in 1 hour = 1/4 …eq. (i)
Because of leak, it requires 4 × 2 = 8 hours
Thus, part of tank filled in 1 hour = 1/8 …eq. (ii)
Let x hours be the time taken by hole to empty the tank,
Thus, part of tank emptied in an hour = 1/x …eq. (iii)
From (i), (ii) & (iii)
Explanation (10) :
LCM of 2, 3 and 4 = 12
In 12 hours, A will finish 6 exercises
B will finish 4 exercises
C will finish 3 exercises
i.e., in 12 hours they will finish 13 exercises
So, in 84 hours they will finish 91 exercises
In next 9 hours, A will finish 4 exercises
B will finish 3 exercises
C will finish 2 exercises
So, they will complete 100 exercises in 93 hours.
Note: Since, they cannot share each-others work so B will take completely 9 hours to make 3 shawls, even when A and C stay idle for4 the last 1 hour till B completes his last exercise.
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