Time and Work: Practice Questions for Competitive Exams

Answers to Time and Work Questions:

1. A can complete a job in 12 days. B can complete the same job in 18 days. How long will they take to complete the job together?

• Answer: $$\text{Time together} = \frac{1}{\frac{1}{12} + \frac{1}{18}} = \frac{1}{\frac{3}{36} + \frac{2}{36}} = \frac{1}{\frac{5}{36}} = 7.2 \, \text{days}$$Time together=121​+181​1​=363​+362​1​=365​1​=7.2days

2. A and B can do a piece of work in 6 and 9 days respectively. How long will it take for them to complete the work together?

• Answer: $$\text{Time together} = \frac{1}{\frac{1}{6} + \frac{1}{9}} = \frac{1}{\frac{5}{18}} = 3.6 \, \text{days}$$Time together=61​+91​1​=185​1​=3.6days

3. If A works twice as fast as B, and together they complete a job in 12 days, how long would A take to finish the work alone?

• Answer:
  Let $A = 2B$A=2B.
  Together, they take 12 days: $$\frac{1}{x} + \frac{1}{\frac{x}{2}} = \frac{1}{12}$$x1​+2x​1​=121​ Solving gives: $x = 24$x=24
  So, A would take 24 days to finish the work alone.

4. A can finish a work in 20 days. B can finish it in 30 days. How long will they take to finish the work together?

• Answer: $$\text{Time together} = \frac{1}{\frac{1}{20} + \frac{1}{30}} = \frac{1}{\frac{5}{60}} = 12 \, \text{days}$$Time together=201​+301​1​=605​1​=12days

5. A and B can complete a task in 20 and 30 days respectively. How long will it take for them to complete the task if they work alternately?

• Answer:
  The time taken when working alternately is calculated by taking their individual rates and adding them.
  In one cycle (one day of A’s work + one day of B’s work), they complete: $$\frac{1}{20} + \frac{1}{30} = \frac{5}{60} = \frac{1}{12}$$201​+301​=605​=121​ Thus, in one cycle (2 days), they complete $\frac{1}{12}$121​ of the task.
  Total time = $12 \times 2 = 24 \, \text{days}$12×2=24days.

6. A and B together can complete a work in 12 days and 18 days respectively. If they work together for 6 days, how much of the work is left?

• Answer: $$\text{Combined rate} = \frac{1}{12} + \frac{1}{18} = \frac{5}{36}$$Combined rate=121​+181​=365​ In 6 days, they complete: $$\frac{5}{36} \times 6 = \frac{30}{36} = \frac{5}{6}$$365​×6=3630​=65​ Thus, the remaining work is $1 – \frac{5}{6} = \frac{1}{6}$1−65​=61​.

7. A can complete a work in 10 days, and B can complete it in 15 days. After working together for 4 days, how much work is left?

• Answer:
  Combined rate = $\frac{1}{10} + \frac{1}{15} = \frac{1}{6}$101​+151​=61​.
  Work done in 4 days = $\frac{1}{6} \times 4 = \frac{2}{3}$61​×4=32​.
  Work left = $1 – \frac{2}{3} = \frac{1}{3}$1−32​=31​.

8. A can complete a work in 8 hours, B in 12 hours, and C in 15 hours. How long will it take for them to complete the work together?

• Answer:
  Combined rate = $\frac{1}{8} + \frac{1}{12} + \frac{1}{15} = \frac{15}{120} + \frac{10}{120} + \frac{8}{120} = \frac{33}{120} = \frac{11}{40}$81​+121​+151​=12015​+12010​+1208​=12033​=4011​.
  Time taken = $\frac{1}{\frac{11}{40}} = \frac{40}{11} \approx 3.64 \, \text{hours}$4011​1​=1140​≈3.64hours.

9. A and B together can complete a work in 6 days. If A works alone for 2 days, how many more days will B take to complete the remaining work?

• Answer:
  Work done by A in 2 days = $\frac{2}{6} = \frac{1}{3}$62​=31​.
  Remaining work = $1 – \frac{1}{3} = \frac{2}{3}$1−31​=32​.
  Time taken by B to complete the remaining work = $\frac{\frac{2}{3}}{\frac{1}{6}} = 4 \, \text{days}$61​32​​=4days.

10. If A can complete a work in 12 days and B can complete it in 18 days, how many days will they take to finish half of the work together?

• Answer:
  Combined rate = $\frac{1}{12} + \frac{1}{18} = \frac{5}{36}$121​+181​=365​.
  Time to complete half the work = $\frac{\frac{1}{2}}{\frac{5}{36}} = \frac{36}{10} = 3.6 \, \text{days}$365​21​​=1036​=3.6days.

11. A, B, and C can complete a work in 10, 15, and 20 days, respectively. How long will it take for all three to finish the work together?

• Answer:
  Combined rate = $\frac{1}{10} + \frac{1}{15} + \frac{1}{20} = \frac{6}{60} + \frac{4}{60} + \frac{3}{60} = \frac{13}{60}$101​+151​+201​=606​+604​+603​=6013​.
  Time taken = $\frac{1}{\frac{13}{60}} = \frac{60}{13} \approx 4.62 \, \text{days}$6013​1​=1360​≈4.62days.

12. If 3 people, A, B, and C, can complete a work in 4 days, 6 days, and 12 days, respectively, how long will it take for A to complete the work alone if they work together for 2 days?

• Answer:
  Combined rate for 2 days = $\frac{1}{4} + \frac{1}{6} + \frac{1}{12} = \frac{7}{12}$41​+61​+121​=127​.
  Work done in 2 days = $\frac{7}{12}$127​.
  Remaining work = $1 – \frac{7}{12} = \frac{5}{12}$1−127​=125​.
  A’s rate is $\frac{1}{4}$41​.
  Time taken by A to complete the remaining work = $\frac{\frac{5}{12}}{\frac{1}{4}} = \frac{5}{3} = 1.67 \, \text{days}$41​125​​=35​=1.67days.

13. A can complete a work in 6 days, B in 8 days, and C in 12 days. If they work together for 2 days, how long will it take for C to finish the remaining work alone?

• Answer:
  Combined rate = $\frac{1}{6} + \frac{1}{8} + \frac{1}{12} = \frac{7}{24}$61​+81​+121​=247​.
  Work done in 2 days = $\frac{7}{24} \times 2 = \frac{7}{12}$247​×2=127​.
  Remaining work = $1 – \frac{7}{12} = \frac{5}{12}$1−127​=125​.
  C’s rate is $\frac{1}{12}$121​.
  Time taken by C to finish the remaining work = $\frac{\frac{5}{12}}{\frac{1}{12}} = 5 \, \text{days}$121​125​​=5days.

14. If A and B can do a job in 8 days, B and C can do the same job in 12 days, and C and A can do it in 14 days, how many days will A, B, and C take to finish the job together?

• Answer:
  Use the system of equations method. $$A + B = \frac{1}{8}, \quad B + C = \frac{1}{12}, \quad C + A = \frac{1}{14}$$A+B=81​,B+C=121​,C+A=141​ Adding these three equations: $$2A + 2B + 2C = \frac{1}{8} + \frac{1}{12} + \frac{1}{14}$$2A+2B+2C=81​+121​+141​ Solving the equation gives: $$A + B + C = \frac{1}{4} \quad \text{(Time taken for all to finish the work together)} = 4 \, \text{days}$$A+B+C=41​(Time taken for all to finish the work together)=4days

15. A can do a piece of work in 10 hours. B takes 12 hours, and C takes 15 hours. If they work together for 6 hours, how much work is completed?

• Answer:
  Combined rate = $\frac{1}{10} + \frac{1}{12} + \frac{1}{15} = \frac{1}{4}$101​+121​+151​=41​.
  Work done in 6 hours = $\frac{1}{4} \times 6 = \frac{3}{2}$41​×6=23​.

16. A is paid ₹100 for 10 hours of work. How much will A be paid for 15 hours of work?

• Answer:
  Rate of payment = $\frac{100}{10} = ₹10$10100​=₹10 per hour.
  For 15 hours, A will be paid $10 \times 15 = ₹150$10×15=₹150.

17. If 5 men can complete a task in 8 days, how long will 3 men take to complete the same task?

• Answer:
  Total work done by 5 men in 8 days = $5 \times 8 = 40$5×8=40 men-days.
  Time taken by 3 men to complete the work = $\frac{40}{3} = 13.33 \, \text{days}$340​=13.33days.

18. A works for 5 hours a day and B works for 6 hours a day. If A completes a task in 10 days and B completes it in 12 days, how long will it take for both A and B working together to complete the task?

• Answer:
  A’s rate = $\frac{1}{10}$101​ of the task per day.
  B’s rate = $\frac{1}{12}$121​ of the task per day.
  Combined rate = $\frac{1}{10} + \frac{1}{12} = \frac{11}{60}$101​+121​=6011​.
  Time taken together = $\frac{1}{\frac{11}{60}} = \frac{60}{11} \approx 5.45 \, \text{days}$6011​1​=1160​≈5.45days.

19. If 4 men can complete a work in 24 days, how many men are required to complete the same work in 12 days?

• Answer:
  Work done by 4 men in 24 days = $4 \times 24 = 96$4×24=96 men-days.
  Time required by $x$x men to complete the same work in 12 days = $x \times 12 = 96$x×12=96.
  Solving gives $x = 8$x=8.

20. A can do a piece of work in 15 days and B in 20 days. They work together for 5 days. How much work is left?

Answer:
Combined rate = $\frac{1}{15} + \frac{1}{20} = \frac{7}{60}$151​+201​=607​.
Work done in 5 days = $\frac{7}{60} \times 5 = \frac{35}{60} = \frac{7}{12}$607​×5=6035​=127​.
Work left = $1 – \frac{7}{12} = \frac{5}{12}$1−127​=125​.