Quantitative Aptitudeमात्रात्मक योग्यता · समय, चाल और दूरी
Time, Speed and Distanceसमय, चाल और दूरीquestions and answersप्रश्न और उत्तर
Speed questions test whether you can choose the right frame: what moves, relative to what, and over what distance.
Unlimitedअसीमितfresh questionsनए प्रश्न
Answersउत्तरalways one tap awayहमेशा एक टैप दूर
1subtopicउप-टॉपिक
SSC CGL ~1
IBPS PO ~1
TCS NQT ~2
Practice questions are in English for now.अभ्यास के प्रश्न अभी अंग्रेज़ी में हैं।
How time, speed and distance worksसमय, चाल और दूरी को समझिए
Average speed is total distance divided by total time. For two equal distances at speeds x and y it is 2xy/(x + y), which is always less than the simple average.
Two people walking towards each other close the gap at the sum of their speeds; in a chase the gap closes at the difference.
Ratios are a shortcut: for a fixed distance, time is inversely proportional to speed.
Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।
Mental mathsमानसिक गणितRarely taughtकम सिखाई जाने वाली✓ Checked on 576 cases✓ 576 मामलों पर जाँची गई
Average speed = plain average − (difference)² / (2 × sum)
Use it when:कब इस्तेमाल करें: Equal distances at two speeds (a round trip, or two halves of a journey).
Take the plain average (x + y)/2.
Subtract (x − y)² / (2(x + y)).
Exampleउदाहरण
Goes at 40 km/h, returns at 60 km/h
→ 50 − 400/200 = 48 km/h
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: (x + y)/2 − 2xy/(x + y) = ((x + y)² − 4xy) / (2(x + y)) = (x − y)² / (2(x + y)). So the harmonic mean is always below the plain average by exactly that gap.
Limits:सीमाएँ: Only for equal distances. For equal times the average speed is the plain average.
Formulaसूत्र✓ Checked on 96 cases✓ 96 मामलों पर जाँची गई
Times after meeting give the speed ratio
Use it when:कब इस्तेमाल करें: Two trains start towards each other; after they meet, one takes a hours and the other b hours to finish.
Speed of first : speed of second = √b : √a.
Exampleउदाहरण
After meeting, A takes 9 h and B takes 4 h
→ A : B = √4 : √9 = 2 : 3
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: Before meeting both run the same time t. A covers what B still has to run, so u·t = v·b and v·t = u·a; dividing gives (u/v)² = b/a.
Limits:सीमाएँ: Both must start at the same moment.
Mental mathsमानसिक गणित✓ Checked on 12 cases✓ 12 मामलों पर जाँची गई
Multiples of 18 km/h are whole m/s
Use it when:कब इस्तेमाल करें: Any train question with speed in km/h and length in metres.
Examiners choose these speeds on purpose; spot them and skip the 5/18 step.
Exampleउदाहरण
72 km/h in m/s
→ 20 m/s
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: 1 km/h = 1000 m / 3600 s = 5/18 m/s, so 18k km/h = 5k m/s.
Limits:सीमाएँ: Other speeds still need × 5/18.
Solved examplesहल किए गए उदाहरण
Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।
Example 1उदाहरण 1 · Relative speed, meeting point and average speed · Easyआसान
Fatima drives from Pune to Guwahati at 30 km/h and returns by the same road at 20 km/h. What is the average speed for the whole journey?
25 km/h
24 km/h
28 km/h
21 km/h
Answer:उत्तर:24 km/h
Average speed = 2 × 30 × 20/(30 + 20)
= 1200/50 = 24 km/h.
Example 2उदाहरण 2 · Relative speed, meeting point and average speed · Mediumमध्यम
Kolkata and Dhanbad are 300 km apart. A bus leaves Kolkata for Dhanbad at 35 km/h and, at the same time, a car leaves Dhanbad for Kolkata at 40 km/h. After how many hours do they meet?
3 hours
4 hours
5 hours
8 hours
Answer:उत्तर:4 hours
Relative speed = 35 + 40 = 75 km/h.
Time = 300 ÷ 75 = 4 hours.
Example 3उदाहरण 3 · Relative speed, meeting point and average speed · Hardकठिन
A thief escapes from Chandni Chowk on a bike at 15 km/h. 2 hours later, a police jeep starts chasing him from the same place at 21 km/h. How many hours after the jeep starts will it catch the thief?
4 hours
5 hours
6 hours
8 hours
Answer:उत्तर:5 hours
Head start = 15 × 2 = 30 km.
Relative speed = 21 − 15 = 6 km/h.
Time = 30 ÷ 6 = 5 hours.
Example 4उदाहरण 4 · Relative speed, meeting point and average speed · Mediumमध्यम
Hyderabad and Vijayawada are 675 km apart. A bus leaves Hyderabad for Vijayawada at 60 km/h and, at the same time, a car leaves Vijayawada for Hyderabad at 75 km/h. How far from Hyderabad (in km) do they meet?
250 km
300 km
350 km
400 km
Answer:उत्तर:300 km
Relative speed = 60 + 75 = 135 km/h.
Time = 675 ÷ 135 = 5 hours.
Bus covers 60 × 5 = 300 km from Hyderabad.
Example 5उदाहरण 5 · Relative speed, meeting point and average speed · Mediumमध्यम
Kolkata and Dhanbad are 420 km apart. A bus leaves Kolkata for Dhanbad at 60 km/h and, at the same time, a car leaves Dhanbad for Kolkata at 45 km/h. How far from Kolkata (in km) do they meet?
180 km
240 km
260 km
290 km
Answer:उत्तर:240 km
Relative speed = 60 + 45 = 105 km/h.
Time = 420 ÷ 105 = 4 hours.
Bus covers 60 × 4 = 240 km from Kolkata.
Example 6उदाहरण 6 · Relative speed, meeting point and average speed · Mediumमध्यम
Bengaluru and Mysuru are 290 km apart. A bus leaves Bengaluru for Mysuru at 80 km/h and, at the same time, a car leaves Mysuru for Bengaluru at 65 km/h. How far from Bengaluru (in km) do they meet?
130 km
160 km
190 km
200 km
Answer:उत्तर:160 km
Relative speed = 80 + 65 = 145 km/h.
Time = 290 ÷ 145 = 2 hours.
Bus covers 80 × 2 = 160 km from Bengaluru.
Common mistakesआम गलतियाँ
Taking the plain average of two speeds.
Using the sum of speeds in a chase.
Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न
Why is average speed not (x + y)/2?
Because you spend more time at the slower speed. Use total distance / total time.
What is relative speed?
The speed of one object as seen from the other: the sum if they move towards each other, the difference if in the same direction.
Are trains and boats part of this topic?
Yes. They are special cases with their own pages for focused practice.