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Time–Speed–Distance Based Data Sufficiency

Introduction

Time-Speed-Distance (TSD) based Data Sufficiency questions test your ability to determine whether given information is enough to find the missing parameter - time, speed, or distance. You do not need to calculate the final numeric answer; you only check if the data provided can uniquely determine it.

This pattern is critical because many aptitude exams test speed, distance, and time interrelations through sufficiency logic rather than direct computation.

Pattern: Time–Speed–Distance Based Data Sufficiency

Pattern

The key formula is: Distance = Speed × Time.

Each statement provides partial data - like the time taken, speed ratio, or total distance. You must check whether one or both statements are enough to determine the unknown variable.

Step-by-Step Example

Question

What is the speed of the train?
(I) The train covers 120 km in 2 hours.
(II) The train covers 180 km in 3 hours.

Solution

  1. Step 1: Analyze Statement (I)

    Speed = Distance ÷ Time = 120 ÷ 2 = 60 km/h. Hence, (I) alone gives the speed → Sufficient.

  2. Step 2: Analyze Statement (II)

    Speed = 180 ÷ 3 = 60 km/h. Hence, (II) alone also gives the speed → Sufficient.

  3. Final Answer:

    Each statement alone is sufficient

  4. Quick Check:

    Both (I) and (II) independently yield 60 km/h ✅

Quick Variations

1. Given distance and time → find speed.

2. Given speed and distance → find time.

3. Given two ratios (speed ratio and time ratio) → find comparison.

4. Questions involving relative speed, trains, or boats (upstream/downstream).

Trick to Always Use

  • Step 1: Write the TSD formula: D = S × T.
  • Step 2: Express each statement algebraically.
  • Step 3: Check if one statement alone gives both values needed to find the target.
  • Step 4: Combine both only if neither alone gives a unique value.

Summary

Summary

  • Check whether a statement provides both speed and time or one complete relation.
  • Each statement should be tested independently first.
  • Combine only if neither provides a unique, solvable condition.
  • Always verify sufficiency, not the numerical answer itself.

Example to remember:
(I) 120 km in 2 hr → 60 km/h; (II) 180 km in 3 hr → 60 km/h → Each statement alone is sufficient.

Practice

(1/5)
1. What is the speed of a car?<br>(I) The car travels 150 km in 3 hours.<br>(II) The car travels 200 km in 4 hours.
easy
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    Speed = 150 ÷ 3 = 50 km/h → sufficient.

  2. Step 2: Analyze (II)

    Speed = 200 ÷ 4 = 50 km/h → sufficient.

  3. Final Answer:

    Each statement alone is sufficient → Option C

  4. Quick Check:

    Both give 50 km/h ✅
Hint: Speed = Distance ÷ Time; if one statement provides both, it's sufficient.
Common Mistakes: Assuming both statements must be combined even when each provides full data.
2. What is the distance covered by a bus?<br>(I) The bus runs at 60 km/h for 4 hours.<br>(II) The bus covers 240 km in 4 hours.
easy
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Evaluate (I)

    Distance = 60 × 4 = 240 km → sufficient.

  2. Step 2: Evaluate (II)

    Direct distance = 240 km → sufficient.

  3. Final Answer:

    Each statement alone is sufficient → Option C

  4. Quick Check:

    Both yield 240 km ✅
Hint: When both speed and time are given, distance can be found directly.
Common Mistakes: Thinking both statements are required to confirm the same distance.
3. What is the time taken by a cyclist to cover a certain distance?<br>(I) Distance = 90 km, Speed = 30 km/h.<br>(II) The cyclist rides for 3 hours.
medium
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    Distance = 90 km and Speed = 30 km/h ⇒ Time = 90 ÷ 30 = 3 hours. So (I) alone is sufficient.

  2. Step 2: Analyze (II)

    Statement (II) directly states the cyclist rides for 3 hours to cover that certain distance. That is exactly the required time, so (II) alone is sufficient.

  3. Final Answer:

    Each statement alone is sufficient → Option C

  4. Quick Check:

    Both (I) and (II) independently yield time = 3 hours ✅
Hint: If a statement directly gives time or gives both distance and speed, it suffices for time questions.
Common Mistakes: Treating a duration statement as unrelated to the asked distance; misreading 'rides for X hours' as extraneous.
4. What is the speed of the boat in still water?<br>(I) The boat goes 30 km downstream in 2 hours.<br>(II) The speed of the stream is 5 km/h.
medium
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    Downstream speed = 30 ÷ 2 = 15 km/h. This is downstream speed (still water speed + stream speed), so alone it does not give still water speed → insufficient.

  2. Step 2: Analyze (II)

    Stream speed = 5 km/h. Alone this does not give still water speed → insufficient.

  3. Step 3: Combine

    Downstream = still + stream ⇒ still = downstream - stream = 15 - 5 = 10 km/h. Both statements together are necessary.

  4. Final Answer:

    Both statements together are necessary → Option D

  5. Quick Check:

    Downstream 15 - stream 5 = still 10 km/h ✅
Hint: If you have downstream speed and stream speed, still water speed = downstream - stream.
Common Mistakes: Applying (downstream + upstream)/2 without having upstream; confusing formulas when stream data are partial.
5. What is the length of the train?<br>(I) A train running at 80 km/h crosses a platform in 1 minute.<br>(II) The platform length is 1.2 km.
medium
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Convert speed

    80 km/h = 80 × (5/18) = 22.22 m/s.

  2. Step 2: Analyze (I)

    In 60 seconds at 22.22 m/s, the train covers 1,333.2 m (train + platform). Alone, cannot isolate train length → insufficient.

  3. Step 3: Analyze (II)

    Platform length = 1,200 m → insufficient alone.

  4. Step 4: Combine

    Train length = 1,333.2 - 1,200 = 133.2 m → sufficient together.

  5. Final Answer:

    Both statements together are necessary → Option D

  6. Quick Check:

    Total crossing distance minus platform length leaves train length → needs both statements ✅
Hint: Crossing a platform gives train + platform; subtract platform length to isolate train length.
Common Mistakes: Trying to find station distance from platform-crossing data.

Mock Test

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