Learn at My Place/Competitive Exams/CUET UG/Quantitative Aptitude/Time, Speed, Distance & Work

CUET UG / Quantitative Aptitude / Time, Speed, Distance & Work

Time, Speed, Distance, Trains, Boats, Circular Motion, Work & Pipes

Learn this high-yield CUET chapter cluster with concept-first notes, fast formulas, solved examples, and a timed practice route built around motion and work-rate logic.

6 Core SubtopicsSolved Examples4 Sectional Sessions40-Question Mock

Go to Notes Solved Examples Open Practice Tests

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Overview

Why This Chapter Cluster Matters in CUET UG

These chapters are all driven by rate logic. In motion questions the rate is speed. In work questions the rate is daily efficiency. In pipes questions the rate is net fill or net drain.

The fastest exam method is to identify the governing formula first, convert units if needed, and only then calculate.

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Section A

Notes & Concept Builder

Formula clarity + exam shortcuts

1. Time, Speed, and Distance 2. Problems on Trains 3. Boats and Streams 4. Circular Motion 5. Time and Work 6. Pipes and Cisterns

1. Time, Speed, and Distance

Every motion question begins with $\text{Distance} = \text{Speed} \times \text{Time}$ . Once two values are known, the third follows directly.

D = S \times T

CUET often mixes km/hr and m/s, so unit conversion matters.

x\text{ km/hr} = x \times \frac{5}{18}\text{ m/s} \qquad x\text{ m/s} = x \times \frac{18}{5}\text{ km/hr}

For fixed distance, time is inversely proportional to speed. That is why a speed ratio of $a:b$ becomes a time ratio of $b:a$ .

10-second shortcut: For equal-distance round trips, average speed is

\frac{2s_1s_2}{s_1+s_2}

, not the plain average.

2. Problems on Trains

Train questions are distance questions with careful attention to what is being crossed. A pole has no length, a platform does.

\text{Time} = \frac{\text{Length to be crossed}}{\text{Relative Speed}}

Opposite directions mean relative speed adds. Same direction means relative speed is the difference.

Exam habit: Write the crossing distance first: train only, train + platform, or both train lengths.

3. Boats and Streams

If $u$ is the speed in still water and $v$ is the current speed, then downstream gets helped by the stream and upstream gets reduced by it.

\text{Downstream} = u+v \qquad \text{Upstream} = u-v

u = \frac{D+U}{2} \qquad v = \frac{D-U}{2}

10-second shortcut: Still-water speed is the average of downstream and upstream speeds. Current speed is half their difference.

4. Circular Motion

Circular motion is relative speed on a closed track. In the same direction, one runner must gain one full circumference. In opposite directions, speeds add.

\text{Time to meet} = \frac{\text{Circumference}}{|s_1-s_2|} \text{ (same direction)}

\text{Time to meet} = \frac{\text{Circumference}}{s_1+s_2} \text{ (opposite direction)}

If they must meet at the starting point again, use lap times and take the LCM.

5. Time and Work

Time and work is rate arithmetic. If A finishes in $X$ days, then A does $1/X$ of the job each day.

\text{Combined rate} = \frac{1}{X} + \frac{1}{Y}

\text{Two-person shortcut} = \frac{XY}{X+Y}

The cleanest exam method is the LCM-efficiency method, because it turns fractional work into whole-number units.

6. Pipes and Cisterns

Pipes and cisterns is time-and-work with water. Inlet pipes add to the tank. Outlet pipes and leaks subtract from it.

\text{Net rate} = \text{Fill rates} - \text{Drain rates}

Final trap: Check the sign of the net rate before dividing. If it is negative, the tank will not fill.

Solved Practice

Solved Examples

Try first, then reveal the logic

Exam Trap: Most errors here come from choosing the wrong crossing distance or wrong net rate, not from arithmetic.

Example 1. A car covers 180 km in 3 hours. At the same speed, how long for 300 km?

Speed = 60 km/hr. Time = 300/60 = 5 hours.

Example 2. A person walks 24 km at 6 km/hr and returns at 4 km/hr. Average speed?

Equal-distance average speed =

\frac{2 \times 6 \times 4}{6+4} = 4.8

km/hr.

Example 3. A train 240 m long crosses a platform 360 m long in 30 seconds. Find the speed.

Total distance = 600 m. Speed = 600/30 = 20 m/s = 72 km/hr.

Example 4. A train passes a pole in 12 seconds at 90 km/hr. Find the train length.

90 km/hr = 25 m/s. Length = 25 x 12 = 300 m.

Example 5. A boat goes downstream at 12 km/hr and upstream at 8 km/hr. Find current speed.

Current = (12 - 8)/2 = 2 km/hr.

Example 6. A boat travels 30 km downstream in 3 hours and the same distance upstream in 5 hours. Find still-water speed.

Downstream = 10, upstream = 6. Still-water speed = (10 + 6)/2 = 8 km/hr.

Example 7. Two runners on a 600 m track move in the same direction at 8 m/s and 5 m/s. When do they first meet?

Relative speed = 3 m/s. Time = 600/3 = 200 seconds.

Example 8. Two runners on a 400 m track move in opposite directions at 6 m/s and 4 m/s. When do they meet?

Relative speed = 10 m/s. Time = 400/10 = 40 seconds.

Example 9. A can finish a work in 12 days and B in 18 days. How long together?

Combined rate = 1/12 + 1/18 = 5/36. Time = 36/5 days.

Example 10. A takes 15 days and B takes 10 days. They work together for 4 days, then A leaves. How many more days for B?

LCM = 30 units. Together 4 days = 20 units. Remaining = 10 units. B takes 10/3 days.

Example 11. 24 workers can complete a job in 15 days. How many workers are needed to finish it in 9 days?

Total work = 24 x 15 = 360 worker-days. Needed = 360/9 = 40 workers.

Example 12. Pipe A fills a tank in 6 hours and pipe B fills it in 8 hours. Together they fill it in?

Combined rate = 1/6 + 1/8 = 7/24. Time = 24/7 hours.

Example 13. Pipe A fills in 4 hours and pipe B empties in 6 hours. Both opened together. Time to fill?

Net rate = 1/4 - 1/6 = 1/12. So the tank fills in 12 hours.

Example 14. Two inlets fill a tank in 20 and 30 hours, and one outlet empties it in 60 hours. All open together. Time to fill?

Net rate = 1/20 + 1/30 - 1/60 = 1/15. So the tank fills in 15 hours.

Example 15. A man is 20 minutes late at 4 km/hr and 10 minutes early at 5 km/hr. Find the distance.

Difference in time = 30 min = 1/2 hr. So d/4 - d/5 = 1/2, giving d = 10 km.

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Section B

The Test Zone

This chapter has a separate practice route with four sectional sessions and a mixed 40-question mock. Each question uses a 60-second timer to help you build exam pace.

Sectional Tests

Focused sessions for work-rate, pipes, speed-distance-trains, and boats-circular logic.

Open Sectional Tests

Full-Length Mock

A mixed mock with timer logic, answer palette, score, accuracy, and explanation review.

Open Full Mock

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Move straight from chapter-wise questions into a subject test, then loop back into weaker areas instead of ending the session here.

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