Defence Exam > Defence Questions > In a race of 1000 m, A beats B by 100 m or 10...
Start Learning for Free
In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B?
- a)65 seconds
- b)60 seconds
- c)50 seconds
- d)45 seconds
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a...
Let the speed of A and B be ‘a’ and ‘b’ (m/s) respectively
Time taken by B – Time taken by A to cover 1000 m = 10 seconds
⇒ 1000/b – 1000/a = 10 [∵ Time = Distance/Speed]
⇒ In the same time A covers 1000 m, B covers (1000 – 100) = 900 meters
Speed of A/Speed of B = Distance covered by A/Distance covered by B
⇒ a/b = 1000/900
⇒ a = 10b/9
⇒ 1000/b – 1000/ (10b/9) = 10
⇒ 1000/b – 900/b = 10
⇒ 100/b = 10
⇒ b = 10 m/s
⇒ a = 10b/9 = 100/9 m/s
⇒ a = 10b/9
⇒ 1000/b – 1000/ (10b/9) = 10
⇒ 1000/b – 900/b = 10
⇒ 100/b = 10
⇒ b = 10 m/s
⇒ a = 10b/9 = 100/9 m/s
Now B’s speed gets halved after covering 450 m
⇒ Time taken by B = 450/b + 550/ (b/2) = 450/10 + 550/5 = 155 seconds
⇒ Time taken by B (if no injury occurred) = 1000/10 = 100 seconds
⇒ Time taken by A = Time taken by B (without injury) + 10 = 110 seconds
∴ A beat B (during injury) by 155 – 110 = 45 seconds
Most Upvoted Answer
In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a...
Given information:
- In the first race of 1000 m, A beats B by 100 m or 10 seconds.
- In the second race, B gets injured after running 50 m less than half the race length and his speed gets halved.
To find:
By how much time will A beat B in the second race?
Approach:
1. Calculate the speed of A and B in the first race.
2. Calculate the time taken by A and B to complete the first race.
3. Calculate the distance covered by B before getting injured in the second race.
4. Calculate the time taken by B to complete the second race.
5. Calculate the time taken by A to complete the second race.
6. Find the difference in time between A and B in the second race.
Calculation:
1. In the first race, A beats B by 100 m or 10 seconds.
- Let the speed of A be 'Va' and the speed of B be 'Vb'.
- Va = Vb + 100/10 (as A beats B by 100 m or 10 seconds)
- Va = Vb + 10
2. In the first race, the distance is 1000 m.
- Time taken by A to complete the first race = 1000/Va
- Time taken by B to complete the first race = 1000/Vb
3. In the second race, B gets injured after running 50 m less than half the race length.
- Distance covered by B before getting injured = (1000/2) - 50 = 450 m
4. In the second race, due to the injury, the speed of B gets halved.
- New speed of B = Vb/2
5. In the second race, the distance is 1000 m.
- Time taken by B to complete the second race = (450/(Vb/2)) + (550/Vb)
- Time taken by A to complete the second race = 1000/Va
6. Difference in time between A and B in the second race = (1000/Va) - [(450/(Vb/2)) + (550/Vb)]
Simplifying the expression, we get:
Difference in time between A and B in the second race = (1000/Va) - (900/Vb)
Substituting Va = Vb + 10, we get:
Difference in time between A and B in the second race = (1000/(Vb+10)) - (900/Vb)
By substituting reasonable values for Vb, we can evaluate the exact difference in time between A and B in the second race. The correct answer is option 'D' which represents the corresponding time difference.
- In the first race of 1000 m, A beats B by 100 m or 10 seconds.
- In the second race, B gets injured after running 50 m less than half the race length and his speed gets halved.
To find:
By how much time will A beat B in the second race?
Approach:
1. Calculate the speed of A and B in the first race.
2. Calculate the time taken by A and B to complete the first race.
3. Calculate the distance covered by B before getting injured in the second race.
4. Calculate the time taken by B to complete the second race.
5. Calculate the time taken by A to complete the second race.
6. Find the difference in time between A and B in the second race.
Calculation:
1. In the first race, A beats B by 100 m or 10 seconds.
- Let the speed of A be 'Va' and the speed of B be 'Vb'.
- Va = Vb + 100/10 (as A beats B by 100 m or 10 seconds)
- Va = Vb + 10
2. In the first race, the distance is 1000 m.
- Time taken by A to complete the first race = 1000/Va
- Time taken by B to complete the first race = 1000/Vb
3. In the second race, B gets injured after running 50 m less than half the race length.
- Distance covered by B before getting injured = (1000/2) - 50 = 450 m
4. In the second race, due to the injury, the speed of B gets halved.
- New speed of B = Vb/2
5. In the second race, the distance is 1000 m.
- Time taken by B to complete the second race = (450/(Vb/2)) + (550/Vb)
- Time taken by A to complete the second race = 1000/Va
6. Difference in time between A and B in the second race = (1000/Va) - [(450/(Vb/2)) + (550/Vb)]
Simplifying the expression, we get:
Difference in time between A and B in the second race = (1000/Va) - (900/Vb)
Substituting Va = Vb + 10, we get:
Difference in time between A and B in the second race = (1000/(Vb+10)) - (900/Vb)
By substituting reasonable values for Vb, we can evaluate the exact difference in time between A and B in the second race. The correct answer is option 'D' which represents the corresponding time difference.
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B?a)65 secondsb)60 secondsc)50 secondsd)45 secondsCorrect answer is option 'D'. Can you explain this answer?
Question Description
In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B?a)65 secondsb)60 secondsc)50 secondsd)45 secondsCorrect answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B?a)65 secondsb)60 secondsc)50 secondsd)45 secondsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B?a)65 secondsb)60 secondsc)50 secondsd)45 secondsCorrect answer is option 'D'. Can you explain this answer?.
In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B?a)65 secondsb)60 secondsc)50 secondsd)45 secondsCorrect answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B?a)65 secondsb)60 secondsc)50 secondsd)45 secondsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B?a)65 secondsb)60 secondsc)50 secondsd)45 secondsCorrect answer is option 'D'. Can you explain this answer?.
Solutions for In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B?a)65 secondsb)60 secondsc)50 secondsd)45 secondsCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.
Here you can find the meaning of In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B?a)65 secondsb)60 secondsc)50 secondsd)45 secondsCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B?a)65 secondsb)60 secondsc)50 secondsd)45 secondsCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B?a)65 secondsb)60 secondsc)50 secondsd)45 secondsCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B?a)65 secondsb)60 secondsc)50 secondsd)45 secondsCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B?a)65 secondsb)60 secondsc)50 secondsd)45 secondsCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Defence tests.
|
|
Explore Courses for Defence exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup