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Time–Speed–Distance Based Data Sufficiency

Introduction

Time-Speed-Distance (TSD) आधारित Data Sufficiency questions यह test करते हैं कि दिया गया information missing parameter - time, speed या distance - को uniquely determine करने के लिए पर्याप्त है या नहीं। यहाँ final numeric answer निकालने की जरूरत नहीं होती; केवल sufficiency check करनी होती है।

यह pattern महत्वपूर्ण है क्योंकि कई aptitude exams में speed, distance और time के interrelations को direct calculation के बजाय sufficiency logic से test किया जाता है।

Pattern: Time–Speed–Distance Based Data Sufficiency

Pattern

मुख्य formula: Distance = Speed × Time.

हर statement कुछ partial data देता है - जैसे लिया गया समय, speed ratio, या total distance। आपको check करना है कि कौन-सा statement (या दोनों) unknown variable को uniquely determine करने के लिए sufficient है।

Step-by-Step Example

Question

Train की speed क्या है?
(I) Train 120 km दूरी 2 घंटे में तय करती है।
(II) Train 180 km दूरी 3 घंटे में तय करती है।

Solution

  1. Step 1: Statement (I) analyze करें

    Speed = Distance ÷ Time = 120 ÷ 2 = 60 km/h. इसलिए (I) अकेला sufficient है।

  2. Step 2: Statement (II) analyze करें

    Speed = 180 ÷ 3 = 60 km/h. इसलिए (II) अकेला भी sufficient है।

  3. Final Answer:

    Each statement alone is sufficient

  4. Quick Check:

    दोनों independently 60 km/h देते हैं ✅

Quick Variations

1. Distance और time दिए हों → speed निकालने की sufficiency check करें।

2. Speed और distance दिए हों → time determine करने की sufficiency देखें।

3. दो ratios (speed ratio, time ratio) दिए हों → comparison निकालना।

4. Relative speed, trains, boats (upstream/downstream) वाले questions।

Trick to Always Use

  • Step 1: TSD formula लिखें: D = S × T.
  • Step 2: हर statement को algebraic form में लिखें।
  • Step 3: देखें कि क्या अकेला statement target निकालने के लिए दोनों जरूरी values देता है या एक complete relation देता है।
  • Step 4: Combine तभी करें जब दोनों में से कोई भी अकेला sufficient न हो।

Summary

Summary

  • Check करें कि statement speed और time दोनों देता है या complete relation देता है।
  • हर statement को पहले independently test करें।
  • Combine तभी करें जब neither alone unique solution दे।
  • हमेशा sufficiency verify करें - final numeric answer निकालना ज़रूरी नहीं।

याद रखने वाला Example:
(I) 120 km in 2 hr → 60 km/h; (II) 180 km in 3 hr → 60 km/h → दोनों statements अकेले 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.

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