Races and Gamesदौड़ और खेल questions and answersप्रश्न और उत्तर

How races and games worksदौड़ और खेल को समझिए

“A beats B by 20 m in a 100 m race” means that when A crosses the line after 100 m, B has run 80 m. They ran for the same time, so their speeds are in the ratio 100 : 80 = 5 : 4. “A can give B a start of 20 m” in a dead heat says exactly the same thing.

“A beats B by 20 m or by 4 seconds” adds a second fact: B needs 4 more seconds to run the last 20 m. That gives B’s speed (5 m/s), then B’s time for the whole race, and A’s time is 4 seconds less.

With three runners, chain the distances, never the margins. If A beats B by 20 m and B beats C by 10 m in 100 m races, then when A finishes, B has run 80 m and C has run 80 × 90/100 = 72 m, so A wins by 28 m, not 30 m.

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।

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।

1. Example 1उदाहरण 1 · Races: beating, giving a start and dead heats · Easyआसान

   In a 200 m race, Lakshmi can give Fatima a start of 2 m and the race ends in a dead heat. What is the ratio of Lakshmi’s speed to Fatima’s speed?

   1. 100 : 1
   2. 99 : 100
   3. 101 : 100
   4. 100 : 99
   Answer:उत्तर: 100 : 99

   1. In the time Lakshmi runs 200 m, Fatima runs 198 m.
   2. Same time, so speed ratio = distance ratio = 200 : 198.
   3. In lowest terms: 100 : 99.

2. Example 2उदाहरण 2 · Races: beating, giving a start and dead heats · Mediumमध्यम

   In a 100 m race, Harpreet beats Aarav by 8 m or by 1 seconds. How long does Harpreet take to run the 100 m?

   1. 12.5 seconds
   2. 11.5 seconds
   3. 0.09 seconds
   4. 13.5 seconds
   Answer:उत्तर: 11.5 seconds

   1. Aarav runs 8 m in 1 s, so Aarav’s speed = 8 m/s.
   2. Aarav’s time for 100 m = 100/8 = 12.5 s.
   3. Harpreet finishes 1 s earlier: 12.5 − 1 = 11.5 s.

3. Example 3उदाहरण 3 · Races: beating, giving a start and dead heats · Hardकठिन

   In a 200 m race, Fatima can give Ananya a start of 10 m and Aditya a start of 48 m. How much start can Ananya give Aditya in a 200 m race?

   1. 40 m
   2. 160 m
   3. 38 m
   4. 50 m
   Answer:उत्तर: 40 m

   1. In the same time, Ananya runs 190 m and Aditya runs 152 m.
   2. When Ananya runs 200 m, Aditya runs 200 × 152/190 = 160 m.
   3. So Ananya can give Aditya a start of 200 − 160 = 40 m.

4. Example 4उदाहरण 4 · Races: beating, giving a start and dead heats · Mediumमध्यम

   Meera and Fatima run at speeds in the ratio 5 : 4. In a 400 m race, how much start should Meera give Fatima so that the race ends in a dead heat?

   1. 320 m
   2. 80 m
   3. 44.44 m
   4. 100 m
   Answer:उत्तर: 80 m

   1. In the time Meera runs 400 m, Fatima runs 400 × 4/5 = 320 m.
   2. So Fatima must start 400 − 320 = 80 m ahead.

5. Example 5उदाहरण 5 · Races: beating, giving a start and dead heats · Mediumमध्यम

   Ananya runs 10/9 times as fast as Aarav. In a 1000 m race, how much start should Ananya give Aarav so that the race ends in a dead heat?

   1. 900 m
   2. 100 m
   3. 52.63 m
   4. 111.11 m
   Answer:उत्तर: 100 m

   1. In the time Ananya runs 1000 m, Aarav runs 1000 × 9/10 = 900 m.
   2. So Aarav must start 1000 − 900 = 100 m ahead.

6. Example 6उदाहरण 6 · Races: beating, giving a start and dead heats · Mediumमध्यम

   In a 1000 m race, Rohan beats Tenzin by 310 m or by 31 seconds. How long does Rohan take to run the 1000 m?

   1. 131 seconds
   2. 69 seconds
   3. 100 seconds
   4. 13.93 seconds
   Answer:उत्तर: 69 seconds

   1. Tenzin runs 310 m in 31 s, so Tenzin’s speed = 10 m/s.
   2. Tenzin’s time for 1000 m = 1000/10 = 100 s.
   3. Rohan finishes 31 s earlier: 100 − 31 = 69 s.

Common mistakesआम गलतियाँ

• Adding the two margins in a three-runner race; the second margin applies to a shorter distance.
• Comparing the race length with the margin (100 : 20) instead of with the loser’s distance (100 : 80).
• Using the winner’s speed where the question is about the loser, for example in “beats by x m or t seconds”.

Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न