Word Problems
(Work-Rate)
Practice Exercise
Very Easy (Difficulty Level-1):
1. If 10 men can do a job in 20 days, how many days will take 8 men to do the job if they work at the same rate?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
2. Three pipes are used to fill a pool with water. One pipe alone can fill the pool in 9 hours. Another can fill it in 6 hours. The third can fill it in 3 hours. How many minutes will it take to fill this pool if all three pipes are used simultaneously?
(A) 1.63
(B) 11
(C) 54
(D) 56.4
(E) 98
3. Mr. Adil can do a job in 8 days, and his son can do it in 12 days. How long would it take them to do the job if they worked together?
(A) 4.8
(B) 5
(C) 10
(D) 15
(E) 20
4. Working together, 7 identical pumps can empty a pool in 6 hours. Approximately how many hours will it take 4 pumps to empty the same pool?
5. A machine can cut some wood in 6 minutes and a man using a hand saw can do it in 18 minutes. After 4 minutes there is a power shortage and the wood must be cut by hand saw, how many minutes must the man work to complete the task?
(A) 2
(B) 6
(C) 12
(D) 14
(E) 18
6. A and B paint a barn in 3 days. A can do it alone in 5 days. How many days would it take B to do this job alone?
(A) 0.2
(B) 3.2
(C) 5.0
(D) 6.4
(E) 7.5
Easy (Difficulty Level-2):
7. A pipe can fill a swimming pool in h hours. What part of the pool is filled in x hours?
(A) hx
(B) h/x
(C) x/h
(D) h+x
(E) (hx)/2
8. If three secretaries can type six manuscripts in 12 days, how many days will it take two secretaries to type three such manuscripts?
9. Five men can paint a house in 6 days. If two of the men don’t works, what will be the increase in time, in days, required to complete the job?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
10. A regular postal clerk sorts 100 letters in c seconds, while a part-time worker requires p seconds to sort 100 letters. How many seconds will take them to sort 100 letters if they work together?
(A) (p + c )/2
(B) (p + c )/pc
(C) (pc)/ (p + c )
(D) 100(p + c )/pc
(E) (100pc)/(p + c )
11. In a factory, a women work b hours a day and produce c articles each day, if d women are released, how many hours a day will the remaining women have to work to produce c articles each day?
(A) (ab)/d
(B) (ad)/b
(C) (a – b)/b
(D) (ab) /(a – d)
(E) b(a – d) /d
12. Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?
(a) 24
(b) 18
(c) 12
(d) 8
(e) 4
Medium (Difficulty Level-3):
13. If a man earns $200 for his first 40 hours of work in a week and then is paid one and half times is regular hourly rate for any additional hours, how many hours must he work to make $230 in a week?
(a) 4
(b) 5
(c) 6
(d) 44
(e) 45
14. Mr. Ahmed can do a job in 10 days. A helper joins him after 3 days, and together they work for 4 days to complete the task. How many days would it take the helper to do the job alone?
(A) 3
(B) 5
(C) 6
(D) 7
(E) 13 1/3.
15. Mr. Amir can mow his lawn in x hours. After 2 hours it begins to rain. What part of the lawn is left unmoved?
(A) (2 – x)/x
(B) x/2
(C) x –2
(D) (x – 2)/2
(E) (x – 2)/x
16. A master painter can paint a house in m days, and his two workers require w1 and w2 days to paint a house. If master works as fast as the two workers together, find m in terms of w1 and w2.
(A) w1 + w2
(B) (w1 + w2)/ w1w2
(C) (w1w2)/ w1 + w2
(D) w1/w2
(E) w2/w1
17. A mother can do a job as fast as her two daughters working together. If one daughter does the job alone in 3 hours and the other does alone in 6 hours. How many hours does it take the mother to do the job alone?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
18. Working alone, Pump A can empty a certain pool in 40 minutes. Working together, pump A and pump B can empty the pool in 24 minutes. Working alone, how many minutes will it take pump B to empty the pool?
Hard (Difficulty Level-4):
19. A student finishes the first half of an exam in 2/3 of the time it takes him to finish the second half. If the entire exam takes him an hour, how many minutes does he spend on the first half of the exam?
(a) 20
(b) 24
(c) 27
(d) 36
(e) 40
20. Cameron can paint a room in c hours. Cameron and Mackenzie, working together, can paint the room in d hours. In terms of c and d, how long in hours would it take Mackenzie, working alone, to paint the room?
(A) 2d – c
(B) (c + d)⁄cd
(C) (c – d)⁄cd
(D) cd⁄(c + d)
(E) cd⁄(c – d)
21. A hotel began draining its swimming pool at a constant rate at 7am. Beginning at 12pm, the rate tripled because of evaporation. If the pool began completely full and was 3/4 full at 9:30am, at what time was the pool completely empty?
A. 12:45pm
B. 1:20pm
C. 1:40pm
D. 2:10pm
E. 2:15pm
22. A constructor is using three water filling pumps, X,Y, and Z, working together at their respective constant rates to fill an initially empty tank in 9 hours.Pumps X and Y,working together at their respective constant rates can fill the same tank in 10 hours.How many hours will pump Z, working alone at its constant rate, take to fill the same tank?
23. At an auto detailing company, it takes 15 minutes for an employee to service a car and 24 minutes to service a truck. If the company needs to service all 300 trucks and 360 cars on a lot during a six-hour shift, how many employees will it need to complete the job?
A. 35
B. 36
C. 40
D. 42
E. 45
24. Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?
A. 5hrs
B. 6hrs
C. 7hrs
D. 8hrs
E. 9hrs
Very Hard & Tricky (Difficulty Level-5):
25. If 16 teachers or 120 students (each with identical rates) can take 21 days to complete a project on dengue awareness among public. Then how long would it take 7 teachers and 70 boys to finish the same task?
26. Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 2 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
27. Pump A can empty a pool in A minutes, and pump B can empty the same pool in B minutes. Pump A begins emptying the pool for 1 minute before pump B joins. Beginning from the time pump A starts, how many minutes will it take to empty the pool?
28. Reserve tank 1 is capable of holding z gallons of water. Water is pumped into tank 1, which starts off empty, at a rate of x gallons per minute. Tank 1 simultaneously leaks water at a rate of y gallons per minute (where x > y). The water that leaks out of tank 1 drips into tank 2, which also starts out empty. If the total capacity of tank 2 is twice the number of gallons of water actually existing in tank 1 after one minute, does tank 1 fill up before tank 2 given that zy < 2x2 – 4xy + 2y2?
29. Machine A produce bolts at uniform rate of 120 bots every 40 seconds. Machine B produce bolts at a uniform rate of 100 bolts every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?
(A) 22
(B) 25
(C) 28
(D) 32
(E) 56
30. Mr. Umer mowed ¾ of his lawn in 1¼ hours. Mr. Ali, who works twice as fast, finished mowing the lawn. How many minutes did Mr. Ali work?
(A) 12 ½
(B) 16
(C) 25
(D) 38
(E) 50
Answer Sheet:
1. B
2. E
3. A
4. 10.5
5. B
6. E
7. C
8. 9
9. B
10. C
11. D
12. B
13. D
14. C
15. E
16. C
17. B
18. 60
19. B
20. E
21. C
22. 90
23. A
24. E
25. 144⁄7
26. 4⁄9
27. A(B + 1)⁄(A + B)
28. Yes
29. B
30. A