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Ramesh and Somesh are competing in a 100 m race. Initially, Ramesh runs at twice the speed of Somesh for the first fifty m. After the 50 m mark, Ramesh runs at l/4th his initial speed while Somesh continues to run at his original speed. If Somesh catches up with Ramesh at a distance of ‘N ’ m from the finish line, then N is equal to
- a)35
- b)10
- c)45
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Ramesh and Somesh are competing in a 100 m race. Initially, Ramesh run...
This question gives us the freedom to assume any value of speeds of Ramesh and Somesh.
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Let us assume the initial speed of Somesh = 20 m/s, then the initial speed of Ramesh = 40 m/s.
Till 50 m they are running with this speed only.
Time taken by Ramesh in covering 50m = 1.25sec. In the same time Somesh is covering 25m.
After this stage, the speed of Somesh is 20m/s,
whereas speed ofRasmesh = 10 m/s.
Now relative speed = 10m/s and distance = 25m.
At 75m from the starting, both of them will be meeting.
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Ramesh and Somesh are competing in a 100 m race. Initially, Ramesh run...
Given:
- Ramesh and Somesh are competing in a 100 m race.
- Ramesh runs at twice the speed of Somesh for the first fifty m.
- After the 50 m mark, Ramesh runs at l/4th his initial speed while Somesh continues to run at his original speed.
- Somesh catches up with Ramesh at a distance of N m from the finish line.
To find: N
Solution:
Let the speed of Somesh be S and the speed of Ramesh be R.
For the first 50 m:
- Somesh covers 50 m at speed S in time t1 = 50/S.
- Ramesh covers 50 m at speed 2S in time t1 = 50/2S = 25/S.
At the 50 m mark:
- Somesh has covered 50 m in time t1 and has 50 m left to cover.
- Ramesh has covered 50 m in time t1 and has 50 m left to cover.
For the next 50 m:
- Somesh covers 50 m at speed S in time t2 = 50/S.
- Ramesh covers 50 m at speed S/4 in time t2 = 200/S.
Total time taken by Somesh = t1 + t2 = 100/S
Total time taken by Ramesh = t1 + t2 = 25/S + 200/S = 225/S
Let the distance covered by Somesh from the finish line be x.
Then, the distance covered by Ramesh from the finish line is x + N.
As both of them finish at the same time:
- Time taken by Somesh to cover the remaining distance = Time taken by Ramesh to cover the remaining distance
- (100-x)/S = (x+N)/225S
Simplifying the equation:
- 225x + 225N = 10000 - x
- 226x = 10000 - 225N
- x = (10000 - 225N)/226
Since x is the distance covered by Somesh from the finish line, it should be less than or equal to 100 m. Hence, we can write the inequality:
(10000 - 225N)/226 ≤ 100
Solving for N:
- 10000 - 225N ≤ 22600
- -225N ≤ 12600
- N ≥ -56 (Since N has to be a non-negative value)
- N can take any non-negative value, hence the answer is None of these.
Therefore, the correct answer is D.
- Ramesh and Somesh are competing in a 100 m race.
- Ramesh runs at twice the speed of Somesh for the first fifty m.
- After the 50 m mark, Ramesh runs at l/4th his initial speed while Somesh continues to run at his original speed.
- Somesh catches up with Ramesh at a distance of N m from the finish line.
To find: N
Solution:
Let the speed of Somesh be S and the speed of Ramesh be R.
For the first 50 m:
- Somesh covers 50 m at speed S in time t1 = 50/S.
- Ramesh covers 50 m at speed 2S in time t1 = 50/2S = 25/S.
At the 50 m mark:
- Somesh has covered 50 m in time t1 and has 50 m left to cover.
- Ramesh has covered 50 m in time t1 and has 50 m left to cover.
For the next 50 m:
- Somesh covers 50 m at speed S in time t2 = 50/S.
- Ramesh covers 50 m at speed S/4 in time t2 = 200/S.
Total time taken by Somesh = t1 + t2 = 100/S
Total time taken by Ramesh = t1 + t2 = 25/S + 200/S = 225/S
Let the distance covered by Somesh from the finish line be x.
Then, the distance covered by Ramesh from the finish line is x + N.
As both of them finish at the same time:
- Time taken by Somesh to cover the remaining distance = Time taken by Ramesh to cover the remaining distance
- (100-x)/S = (x+N)/225S
Simplifying the equation:
- 225x + 225N = 10000 - x
- 226x = 10000 - 225N
- x = (10000 - 225N)/226
Since x is the distance covered by Somesh from the finish line, it should be less than or equal to 100 m. Hence, we can write the inequality:
(10000 - 225N)/226 ≤ 100
Solving for N:
- 10000 - 225N ≤ 22600
- -225N ≤ 12600
- N ≥ -56 (Since N has to be a non-negative value)
- N can take any non-negative value, hence the answer is None of these.
Therefore, the correct answer is D.
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Ramesh and Somesh are competing in a 100 m race. Initially, Ramesh runs at twice the speed of Somesh for the first fifty m. After the 50 m mark, Ramesh runs at l/4th his initial speed while Somesh continues to run at his original speed. If Somesh catches up withRamesh at a distance of ‘N ’ m from the finish line, then N is equal toa)35b)10c)45d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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Ramesh and Somesh are competing in a 100 m race. Initially, Ramesh runs at twice the speed of Somesh for the first fifty m. After the 50 m mark, Ramesh runs at l/4th his initial speed while Somesh continues to run at his original speed. If Somesh catches up withRamesh at a distance of ‘N ’ m from the finish line, then N is equal toa)35b)10c)45d)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Ramesh and Somesh are competing in a 100 m race. Initially, Ramesh runs at twice the speed of Somesh for the first fifty m. After the 50 m mark, Ramesh runs at l/4th his initial speed while Somesh continues to run at his original speed. If Somesh catches up withRamesh at a distance of ‘N ’ m from the finish line, then N is equal toa)35b)10c)45d)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ramesh and Somesh are competing in a 100 m race. Initially, Ramesh runs at twice the speed of Somesh for the first fifty m. After the 50 m mark, Ramesh runs at l/4th his initial speed while Somesh continues to run at his original speed. If Somesh catches up withRamesh at a distance of ‘N ’ m from the finish line, then N is equal toa)35b)10c)45d)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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