Unit 1: Efficiency and Inlet-Outlet Pipes - Practice Quiz

1 A worker completes a task in 10 days. What is the worker's one-day work rate?

2 A is twice as efficient as B. If B completes a task in 12 days, how many days will A take?

3 If a person becomes 25% more efficient, the time required to complete the same work will generally:

4 Two workers earn wages in the ratio according to their work. If the total wage is , what is the first worker's share?

5 A worker is paid for completing a job in 4 days. What is the daily wage?

6 Wages are usually divided among workers in proportion to their:

7 The chain rule is mainly used when a problem involves:

8 If 4 workers complete a job in 6 days, how many worker-days are required for the job?

9 For the same work, if the number of workers increases, the number of days required generally:

10 A works on Monday, B works on Tuesday, and they continue on alternate days. This arrangement is called:

11 A can complete a job in 4 days and B can complete it in 8 days. If they work on alternate days starting with A, how much work is completed in the first two days?

12 In an alternate work problem, the worker who starts first works on:

13 If a job is completed in 5 days, what fraction of the job is completed per day at a constant rate?

14 A and B together complete a job in 6 days. Their combined one-day work is:

15 If a worker completes of a job in one day at a constant rate, the complete job will take:

16 A pipe that fills a tank is called a(n):

17 A pipe that removes water from a tank is called a(n):

18 A pipe fills of a tank in one hour. How much of the tank does it fill in 2 hours?

19 If a tank is half full, what fraction of the tank is still empty?

20 A pipe fills a tank in 8 hours. How long does it take to fill half the tank at the same rate?

21 A is more efficient than B. If they complete a job together in days, how many days would A alone take to complete it?

22 The efficiencies of A, B, and C are in the ratio . If A and B together complete a task in days, how long will all three take?

23 A worker normally completes a job in days. If the worker's efficiency decreases by , how long will the same job take?

24 A is twice as efficient as B. A works for days and B works for days on the same project. If the total wage is , what is A's share?

25 The efficiencies of A, B, and C are in the ratio . They work for , , and days respectively. How should a total wage of be divided?

26 workers working hours per day for days produce units. How many days will workers working hours per day need to produce units at the same rate?

27 machines operating hours per day produce components in days. How many days will machines operating hours per day take to produce components?

28 A can complete a job in days and B in days. They work on alternate days, beginning with A. In how many days will the job be completed?

29 A can complete a task in days and B in days. They work on alternate days, beginning with B. When will the task be completed?

30 A can finish a job in days and B in days. A works for two consecutive days, and B works every third day in place of A. This pattern repeats. How long will the job take?

31 A can complete a job in days and B in days. They work together for days, after which A leaves. How many total days are needed to finish the job?

32 A and B together can complete a job in days, B and C in days, and C and A in days. How long will all three take working together?

33 A can complete a job in days and B in days. A works alone for days, and then B joins. How long does the entire job take?

34 Two inlet pipes can fill a tank in hours and hours, while an outlet can empty it in hours. If all three are opened together, how long will the empty tank take to fill?

35 An inlet can fill a tank in hours, while an outlet can empty it in hours. The inlet is opened first, and the outlet is opened hours later. How long after the inlet is opened will the tank become full?

36 Inlet A fills a tank in hours, inlet B in hours, and an outlet empties it in hours. All three are opened together, but B is closed after hours. When will the tank be full?

37 Two inlet pipes fill a tank in hours and hours, while an outlet empties it in hours. What fraction of the tank is filled when all three operate for hours?

38 A tank is initially full. An inlet can fill the entire tank in hours, while an outlet can empty it in hours. If both are opened, how long will the tank take to become full?

39 Pipe A can fill a tank in hours and is opened at 8:00 a.m. Pipe B can fill it in hours and is opened at 11:00 a.m. At what time will the tank become full?

40 An inlet fills a tank in hours, and an outlet empties it in hours. They are operated alternately for one hour each, beginning with the inlet. After how many hours will the initially empty tank be full?

41 Worker A is more efficient than worker B. Together they can complete a job in days. After working together for days, A's efficiency decreases by while B's efficiency increases by . How many additional days will they require to finish the job?

42 A and B can complete a job in days, B and C in days, and C and A in days. A and C work together for days, after which B alone completes the remaining work. What is the total time taken?

43 A, B, and C undertake a job for . A and B work together for days, after which C alone finishes the job. A, B, and C can individually complete the job in , , and days, respectively. If wages are divided in proportion to work done, what is C's share?

44 A can complete a job in days and B in days. They work together for days, after which B leaves and A works alone for another days. The unfinished job is then cancelled, and is paid for the work actually completed. If payment is proportional to individual contribution, how much should B receive?

45 Eighteen workers, working hours per day for days, produce components. How many workers, each more efficient than the original workers, are needed to produce components by working hours per day for days?

46 A job can be completed by men or women in days. Sixteen men and women work on it for days. The remaining work is completed by men and women. How many additional days are required?

47 A can complete a job in days and B in days. They work on alternate days, beginning with A. After each has worked on three days, both permanently lose of their original efficiency. In how many days is the job completed?

48 A can finish a job in days and B in days. They work on alternate days beginning with B, except that on every fourth calendar day both work together. In how many days will the job be completed?

49 A and B together can finish a job in days, while A alone can finish it in days. They work together for days, after which B's efficiency permanently decreases by . What is the total time required to complete the job?

50 A can complete a construction job in days, B in days, while C can undo the completed job in days. All three operate for days. C then leaves, and A leaves days later. How long from the start does B take to finish the job?

51 A, B, and C have efficiencies in the ratio . A completes the first one-third of a job, B completes half of the remaining work, and C finishes the rest. If the total elapsed working time is days, for how many days does B work?

52 Pipe A fills a tank in hours, pipe B in hours, and pipe C empties it in hours. A remains open continuously, B is open during alternate one-hour periods beginning with the first hour, and C is open during every third one-hour period. When will an initially empty tank become full?

53 Two inlet pipes can fill a tank in hours and hours, respectively. With a leak open, both pipes together fill it in hours. Starting empty, all three are opened until the tank is full; the slower inlet is then closed. How long does the tank take to become full?

54 A tank is initially full. Inlets A and B, which can fill the whole tank in hours and hours, are opened for hours. A is then closed and an outlet capable of emptying the full tank in hours is opened while B remains open. How long after A and B were first opened will the tank become full?

55 Inlets A and B can fill a tank in hours and hours. They are opened together until the tank is half full. B is then closed and an outlet that can empty a full tank in hours is opened while A remains open. What is the total filling time?

56 An inlet fills a tank in hours, a second inlet fills it in hours, and an outlet empties it in hours. Starting empty, the first inlet works alone for hours. The other inlet and the outlet are then opened without closing the first inlet. When does the tank become full?

57 A can complete a job in days by working hours daily, while B can complete it in days by working hours daily. They work together for hours per day, but on every fifth day only B works. If they start together on day , when is the job completed?

58 Thirty workers are scheduled to complete a job in days by working hours daily. After days, only of the job is complete. Assuming the productivity observed during these days remains unchanged, how many additional workers are needed to complete the remaining job in days at hours daily?

59 A and B can complete a job in days, B and C in days, and C and A in days. A works every day, B joins on every even-numbered day, and C joins on every third day. All work at their normal constant rates. In how many days is the job completed?

60 Inlet A fills a tank in hours and remains open continuously. Inlet B fills it in hours and is open only during the first hour of each repeating three-hour cycle. An outlet empties the tank in hours and is open only during the third hour of each cycle. Starting with an empty tank, when does it become full?