Unit 1: Time, Work and Cisterns - Practice Quiz

1 A worker completes a job in days. What fraction of the job does the worker complete in one day?

2 Ravi can finish a task in days. What part of the task will he finish in days?

3 Which formula correctly relates work, rate of work, and time?

4 A can complete a job in days and B can complete it in days. How long will they take working together?

5 The efficiencies of A and B are in the ratio . If A takes days to finish a job, how many days will B take?

6 Four men complete a job in days. At the same rate, how many days will eight men take?

7 If women can do the same amount of work as children, then women are equivalent to how many children?

8 A and B complete a job together and divide ₹600 in the ratio . What is A's share?

9 A pipe can fill an empty tank in hours. What fraction of the tank does it fill in one hour?

10 An inlet fills a tank in hours, while an outlet empties it in hours. How long will the tank take to fill if both are open?

11 A pipe fills of a tank every hour. What part of the tank will it fill in hours?

12 A tank is full. A pipe fills of the tank per hour. How many more hours are needed to fill it?

13 A can complete a task in days. What fraction of the task remains after A works for days?

14 A finishes a job in days and B finishes it in days. In how many days can they finish it together?

15 A worker completes of a job each day. How many days are required to complete the whole job?

16 If one man does as much work as two women, then three men do as much work as how many women?

17 A works for days and B works for days at the same daily rate. If their total wage is ₹800, what is A's share?

18 An inlet fills a tank in hours, and an outlet empties it in hours. How long will the empty tank take to fill when both are open?

19 A tank is initially full. A pipe adds another of the tank. What fraction of the tank is now full?

20 Five identical pipes fill a tank in hours. How long would one such pipe take to fill the tank alone?

21 A can complete a job in 12 days, while B can complete it in 18 days. How long will they take to complete the job together?

22 A and B together complete a job in 10 days. If A alone can complete it in 15 days, how many days will B alone require?

23 A can finish a job in 20 days. A works alone for 5 days, after which B joins. They finish the remaining work in another 5 days. How long would B alone take to finish the whole job?

24 The efficiencies of A and B are in the ratio . If they complete a job together in 12 days, how long will A alone take?

25 A is 25% more efficient than B. If A completes a task in 16 days, how many days will B require for the same task?

26 If 2 men do the same work as 3 women or 6 children, and 12 men can complete a job in 20 days, how many days will 8 men, 6 women, and 12 children take?

27 Fifteen men can complete a job in 24 days. After working for 8 days, 5 men leave. In how many total days will the job be completed?

28 A, B, and C can individually complete a job in 4, 6, and 12 days, respectively. They work together and earn . What is A's share?

29 Six men and four women work for the same number of days and earn in total. If a man is twice as efficient as a woman, what is the total share of the women?

30 Pipe A fills a tank in 12 hours, and pipe B fills it in 18 hours. If both are opened together, how long will they take to fill the tank?

31 An inlet fills a tank in 10 hours, while an outlet empties a full tank in 15 hours. If both are opened together when the tank is empty, how long will it take to fill?

32 Two pipes can fill a cistern in 8 hours and 12 hours, while a third pipe can empty it in 24 hours. If all three are opened together, how long will the empty cistern take to fill?

33 A pipe fills a tank in 6 hours. It runs alone for 2 hours, and then an outlet is opened. The tank becomes full 8 hours after the inlet was first opened. In how many hours can the outlet empty a full tank?

34 A pipe can fill a tank in 4 hours, but because of a leak it takes 5 hours. How long would the leak alone take to empty the full tank?

35 Pipe A fills a tank in 10 hours and is opened first. After 2 hours, pipe B, which fills the tank in 15 hours, is also opened. How long after A was first opened will the tank be full?

36 Pipe A can fill a tank in 6 hours and pipe B in 8 hours. They are opened alternately for one hour each, starting with A. When will the initially empty tank become full?

37 Sixteen workers, working 9 hours per day, finish a job in 15 days. How many days will 24 workers, each 25% more efficient, take if they work 6 hours per day?

38 A and B together can complete a job in 8 days. The job can also be completed if A works alone for 6 days and B works alone for 12 days. How long will A alone take?

39 A is twice as efficient as B, and B is three times as efficient as C. If all three together complete a job in 18 days, how long will C alone take?

40 A tank is initially one-fourth full. An inlet can fill the entire tank in 8 hours, while an outlet can empty it in 12 hours. If both are opened together, how long will it take to fill the tank completely?

41 A and B can complete a job in 12 days, B and C in 15 days, and C and A in 20 days. All three work together for 4 days. Then A leaves, and B leaves 3 days later. How many days elapse from the start until C completes the remaining work?

42 A is 50% more efficient than B, while B is 25% less efficient than C. If A and C together complete a job in 8 days, how long would B alone take?

43 The daily work of 3 men equals that of 5 women and also that of 8 children. If 8 men and 10 women complete a job in 12 days, how long will 5 men, 8 women, and 16 children take?

44 The efficiencies of A and B are in the ratio , while those of B and C are in the ratio . A, B, and C work for 8, 12, and 6 days respectively. If the total wage is , how should it be divided according to work done?

45 Inlet A fills a tank in 12 hours, inlet B in 18 hours, and outlet C empties it in 24 hours. A is opened initially, B is opened 2 hours later, and C is opened 3 hours after B. If no pipe is subsequently closed, when will the tank become full?

46 An inlet can fill a cistern in 10 hours, while an outlet can empty it in 15 hours. They are opened alternately for one hour each, beginning with the inlet. Assuming the cistern is initially empty, after how much time will it first become full?

47 Inlets A and B can fill a tank in 8 and 12 hours, while a leak can empty it in 24 hours. A and B are opened together until the tank is half full. A is then closed and the leak is opened while B remains open. How long does the entire filling process take?

48 Pipe A fills the first one-third of a tank and pipe B fills the remaining two-thirds in a total of 14 hours. If B instead fills the first one-third and A fills the remaining two-thirds, the total time is 16 hours. How long will both pipes together take to fill the tank?

49 A and B together complete a job in 10 days, A and C in 12 days, and B and C in 15 days. Using the pair-rate formula, how long will A alone take?

50 A can complete a job in 20 days and B in 30 days. They normally work together, but on every third day only A works. If this pattern begins with two days of joint work followed by one day of A working alone, when is the job completed?

51 A and B can complete a job in 18 days, B and C in 24 days, and C and A in 36 days. All three work for 6 days, after which only A and B work for 3 days. C then completes the remaining work alone. What is the total elapsed time?

52 A can complete a job in 24 days at normal efficiency. After working normally for 6 days, A's efficiency increases by 50% for the rest of the job. After 4 more days, B joins A, and they complete the remaining work in 3 days. How long would B alone take?

53 Two men perform as much daily work as three women, and four women perform as much as five children. If 8 men and 12 women finish a job in 15 days, how long will 5 men, 9 women, and 10 children take?

54 A and B can complete a contract individually in 20 and 30 days. They work together for 8 days, after which A alone finishes the contract. If is divided in proportion to actual work done, what is A's share?

55 A tank is initially one-fourth full. Inlet A fills it in 12 hours, inlet B in 18 hours, and an outlet empties it in 24 hours. First, A and the outlet operate until the tank is half full. Then B and the outlet operate until it is three-fourths full. Finally, the outlet is closed and both inlets operate. What is the total time required?

56 A pipe should fill a tank in 8 hours, but because of an unnoticed leak it takes 10 hours. If the tank is three-fifths full when the pipe is closed, how long will the leak take to empty it?

57 Twelve men can complete a job in 20 days. After 5 days, 4 men leave; after another 5 days, 6 women join the remaining men. If two women perform the same daily work as one man, how many days from the start are required to finish the job?

58 A requires 10 fewer days than B to finish a job. Together they can finish it in 12 days. If A first works alone for 5 days and then B joins, how many days in total are needed?

59 Inlet A fills a tank in 12 hours and remains open continuously. In each repeating 3-hour cycle, inlet B, which fills the tank in 18 hours, is open only during the first hour; outlet C, which empties the tank in 9 hours, is open only during the second and third hours. Starting with an empty tank, when will it become full?

60 A and B together can complete a job in 12 days. A works alone for 3 days, B then works alone for 7 days, and finally they work together for 6 days to complete the job exactly. How long would A alone take?