Time and Work Quiz: Pipes and Cisterns Practice

Spoilers! These are the Starter quiz’s answers. Easy, Medium, Hard and Mixed rounds show their own answers when you finish.

1. A can finish a job in 12 days and B in 18 days. Working together, in how many days will they finish it?

   • 7.2 days
   • 7.5 days
   • 6 days
   • 8 days

   Answer: 7.2 days. Together = ab/(a + b) = 12 × 18/30 = 7.2 days. (LCM 36 units: A 3/day, B 2/day, so 36/5 = 7.2.)

2. A and B together can finish a work in 10 days. A alone can do it in 15 days. How long will B alone take?

   • 25 days
   • 20 days
   • 30 days
   • 36 days

   Answer: 30 days. B's daily rate = 1/10 − 1/15 = 1/30, so B alone takes 30 days.

3. A is twice as efficient as B. Together they finish a job in 14 days. In how many days can A alone finish it?

   • 28 days
   • 21 days
   • 18 days
   • 24 days

   Answer: 21 days. Efficiencies 2:1 give 3 units a day; work = 3 × 14 = 42 units. A alone: 42/2 = 21 days.

4. 12 men can complete a piece of work in 20 days. How many days will 15 men take to complete the same work?

   • 15 days
   • 18 days
   • 24 days
   • 16 days

   Answer: 16 days. Man-days stay constant: 12 × 20 = 240, so 240/15 = 16 days.

5. 10 men working 8 hours a day finish a job in 12 days. In how many days will 16 men working 6 hours a day finish the same job?

   • 10 days
   • 12 days
   • 9 days
   • 8 days

   Answer: 10 days. M1D1H1 = M2D2H2: 10 × 12 × 8 = 16 × D × 6, so 960 = 96D and D = 10 days.

6. Pipes A and B can fill a tank in 20 minutes and 30 minutes, while pipe C can empty it in 15 minutes. If all three are opened together on an empty tank, when will it be full?

   • 50 minutes
   • 60 minutes
   • 45 minutes
   • 80 minutes

   Answer: 60 minutes. Take 60 units: A +3, B +2, C −4 per minute, net +1. The tank fills in 60 minutes.

7. A can do a work in 16 days and B in 24 days. They work together for 4 days and then A leaves. In how many more days will B finish the work?

   • 12 days
   • 16 days
   • 14 days
   • 10 days

   Answer: 14 days. LCM 48 units: A 3/day, B 2/day. In 4 days they do 20 units; B does the remaining 28 units in 14 days.

8. A pipe can fill a tank in 6 hours. Because of a leak at the bottom, it takes 8 hours to fill. In how long can the leak alone empty the full tank?

   • 20 hours
   • 14 hours
   • 48 hours
   • 24 hours

   Answer: 24 hours. Leak rate = 1/6 − 1/8 = 1/24 per hour, so it empties the full tank in 24 hours. Shortcut: ab/(b − a) = 48/2.

9. A and B can do a job in 6 days and 9 days respectively. They do it together and are paid Rs 4,500. What is A's share?

   • Rs 2,700
   • Rs 2,250
   • Rs 3,000
   • Rs 1,800

   Answer: Rs 2,700. Working the same days, pay is in the ratio of efficiency = 1/6 : 1/9 = 3:2. A gets 3/5 of 4,500 = Rs 2,700.

10. A and B can do a work in 12 days, B and C in 15 days, and C and A in 20 days. In how many days can A, B and C together do it?

    • 8 days
    • 10 days
    • 12 days
    • 9 days

    Answer: 10 days. Adding the three pair-rates counts each person twice: 1/12 + 1/15 + 1/20 = 1/5 = 2(A + B + C). So A + B + C = 1/10: 10 days.