Unit 1: Time and Work, Pipes and Cisterns - Practice Quiz

1 If a person completes a piece of work in days, the fraction of work completed in one day is:

2 A can complete a job in days. How many days will A take to complete the whole job alone?

3 The basic formula for work is:

4 A can complete a job in days and B can complete it in days. If they work together, how many days will they take?

5 A completes a job in days and B completes it in days. What part of the job do they complete together in one day?

6 If A is twice as efficient as B, then A takes what fraction of B's time to complete the same work?

7 A worker completes units of work in hours. What is the worker's efficiency per hour?

8 If man does the same work as women, how many women are equivalent to men?

9 If woman can complete the same work as children, then women are equivalent to how many children?

10 A worker earns for days of work. What is the wage per day?

11 Two workers share in the ratio . What is the larger share?

12 A pipe that fills a tank is called:

13 An inlet fills a tank in hours, while an outlet empties it in hours. How much of the tank is filled in one hour when both are open?

14 A pipe fills of a tank in one hour. How much of the tank will it fill in hours?

15 A tank is full. What fraction of the tank is empty?

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

17 A can finish a job in days. How much work will A complete in days?

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

19 A can complete a job in days and B can complete it in days. How much work do they complete together in one day?

20 An inlet fills a tank in hours and an outlet empties it in hours. If both are opened together, how long will it take to fill the tank?

21 A can complete a piece of work in days, while B can complete it in days. How long will they take to complete the work together?

22 A and B together complete a job in days. If A alone can complete it in days, how long would B alone take?

23 The efficiencies of A and B are in the ratio . If A completes a job in days, how many days will B take to complete the same job?

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

25 Two men can do as much work as three women. If men can complete a job in days, how long will men and women take?

26 The work capacities satisfy men women children. If men, women, and children finish a job in days, how long will men, women, and children take?

27 A and B are paid for a job. A works for days with efficiency units per day, while B works for days with efficiency units per day. What is A's share?

28 A and B complete a job together and receive . If their efficiencies are in the ratio , what amount should B receive?

29 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?

30 Two pipes fill a tank in hours and hours. They are opened together, and after hours an outlet that can empty the full tank in hours is also opened. When will the tank be full?

31 A pipe can fill an empty tank in hours. What fraction of the tank will remain empty after the pipe has operated for hours?

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

33 A pipe normally fills a tank in hours. Because of a leak, the tank fills in hours. How long would the leak take to empty the full tank by itself?

34 A full tank has two outlet pipes that can empty it separately in hours and hours. If both outlets are opened together, how long will they take to empty the tank?

35 If A completes a job in days and B completes it in days, which expression gives the number of days required when they work together?

36 Fifteen workers, working hours per day, complete a project in days. How many days will equally efficient workers, working hours per day, require?

37 Twenty-four workers can complete a project in days. After working for days, workers leave. How many days from the start will the project take?

38 A is more efficient than B. Working together, they complete a job in days. How long would B take to complete it alone?

39 A can complete a job in days and B in days. They work together for days, after which A leaves and B finishes the job. If they receive , what is A's share based on work done?

40 An inlet fills a tank in hours and an outlet empties it in hours. They are opened alternately for one hour each, starting with the inlet. How long will an empty tank take to become full?

41 A can complete a work in 12 days and B in 18 days. They work together for 4 days, after which C joins them. If A, B, and C together can complete the entire work in days, how long will the work take in total?

42 A and B work on alternate days, beginning with A. A alone completes the work in 10 days and B alone in 15 days. How many days are required to complete the work?

43 A and B together complete a work in 8 days, B and C together in 12 days, and C and A together in 24 days. In how many days can A alone complete the work?

44 A is 50% more efficient than B. Working together, they complete a task in 12 days. How many days would A alone require?

45 Two men are as efficient as three women, and three women are as efficient as four children. A team of 4 men, 6 women, and 10 children completes a work in 15 days. How many days will a team of 8 men, 6 women, and 12 children take?

46 A, B, and C have efficiencies in the ratio . They work for 5, 6, and 8 days respectively on a project worth . If wages are proportional to work done, what is B's share?

47 An inlet fills a tank in 24 hours, another fills it in 36 hours, and an outlet empties it in 48 hours. All three are opened for 8 hours, after which the outlet is closed. How long does it take to fill the tank completely?

48 An inlet fills of a tank in 2 hours, while an outlet empties of the tank in 3 hours. The tank is initially full. If both are opened together for 4 hours, how much more time is needed to fill the tank completely?

49 A can complete a work in 15 days and B in 20 days. They work together for 6 days, after which A leaves. How many additional days does B need to finish the remaining work?

50 A is twice as efficient as B, and B is three times as efficient as C. Together, they complete a work in 8 days. How many days would A alone take?

51 Eight men complete a task in 18 days. After 6 days, 2 men leave, and the efficiency of each remaining man increases by 25%. How many total days are needed to finish the task?

52 A, B, and C have efficiencies in the ratio . They work for 6, 8, and 10 days respectively on a project worth . If wages are proportional to work done, what is C's wage?

53 An inlet fills a tank in 16 hours, a second inlet in 24 hours, and an outlet empties it in 48 hours. The two inlets operate for 3 hours, after which the second inlet is closed and the outlet is opened. How much total time is needed to fill the tank?

54 A tank is initially full. An inlet fills of the tank per hour, and an outlet empties per hour. If both operate for 5 hours, what fraction of the tank is full?

55 A completes of a work in 4 days, while B completes of it in 6 days. What fraction of the work will they complete together in 5 days?

56 A can complete a work in 24 days and B in 36 days. A works every day, while B works on alternate days beginning on day 2. On which day will the work be completed?

57 A and B together can complete a task in 10 days, while A alone can complete it in 15 days. They work together for 4 days, after which A's efficiency decreases by 20% and both continue working. How many days are required in total?

58 The daily work rates of A and B are in the ratio . If A works 4 days and B works 7 days, together they complete of a project. How many days would A alone require for the whole project?

59 An inlet fills a tank in 30 hours, a second inlet in 40 hours, and an outlet empties it in 60 hours. The first two operate for 4 hours, followed by 2 hours with only the outlet open. This 6-hour pattern repeats. How long will it take to fill the tank completely?

60 A is 25% less efficient than B. Together they complete a work in 20 days. If A works alone for the first 8 days and B completes the remainder, how many days does B work?