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DIRECTIONS for the question: Solve the following question and mark the best possible option.
26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court. All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest. A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.
Q. How many seconds after the start of the race, will all 26 be at the starting point together?
- a)400
- b)500
- c)600
- d)800
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
Let Z’s speed be x.
Let the difference of speed between Z and Y (or A and B) be d.
A’s speed will be x + 25d
So, 100/ (x + 25d – x) = 20
Or 100/25d = 20
Or d = 0.2 m/s
Also M’s speed will be x + 13d.
Converting 52 minutes and 5 seconds to seconds, we get = 3125 s.
After running 3125 s, M finishes 10,000 m.
So, 3125 (x + 13d) = 10,000.
► 3125x = 10,000 – 3125 × 13 × 0.2 = 10,000 – 8,125 = 1,875
So x = 2500 / 3125 = 0.6 m/s.
So the speeds of Z to A are 0.6, 0.8, 1, 1.2, 1.4, …
Time taken for completing one round for Z to A –
► 100/0.6, 100/0.8, 100/1…
The required answer is LCM (100/0.6, 100/0.8, 100/1…)
The LCM of fractions is the LCM of numerator divided by HCF of denominators
Let the difference of speed between Z and Y (or A and B) be d.
A’s speed will be x + 25d
So, 100/ (x + 25d – x) = 20
Or 100/25d = 20
Or d = 0.2 m/s
Also M’s speed will be x + 13d.
Converting 52 minutes and 5 seconds to seconds, we get = 3125 s.
After running 3125 s, M finishes 10,000 m.
So, 3125 (x + 13d) = 10,000.
► 3125x = 10,000 – 3125 × 13 × 0.2 = 10,000 – 8,125 = 1,875
So x = 2500 / 3125 = 0.6 m/s.
So the speeds of Z to A are 0.6, 0.8, 1, 1.2, 1.4, …
Time taken for completing one round for Z to A –
► 100/0.6, 100/0.8, 100/1…
The required answer is LCM (100/0.6, 100/0.8, 100/1…)
The LCM of fractions is the LCM of numerator divided by HCF of denominators
Hence = LCM (100, 100, 100…) / HCF (0.6, 0.8, 1.0,… ) = 100/0.2 = 500 s.
Most Upvoted Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
Let Z’s speed be x.
Let the difference of speed between Z and Y (or A and B) be d.
A’s speed will be x + 25d
So, 100/ (x + 25d – x) = 20
Or 100/25d = 20
Or d = 0.2 m/s
Also M’s speed will be x + 13d.
Converting 52 minutes and 5 seconds to seconds, we get = 3125 s.
After running 3125 s, M finishes 10,000 m.
So, 3125 (x + 13d) = 10,000.
► 3125x = 10,000 – 3125 × 13 × 0.2 = 10,000 – 8,125 = 1,875
So x = 2500 / 3125 = 0.6 m/s.
So the speeds of Z to A are 0.6, 0.8, 1, 1.2, 1.4, …
Time taken for completing one round for Z to A –
► 100/0.6, 100/0.8, 100/1…
The required answer is LCM (100/0.6, 100/0.8, 100/1…)
The LCM of fractions is the LCM of numerator divided by HCF of denominators
Let the difference of speed between Z and Y (or A and B) be d.
A’s speed will be x + 25d
So, 100/ (x + 25d – x) = 20
Or 100/25d = 20
Or d = 0.2 m/s
Also M’s speed will be x + 13d.
Converting 52 minutes and 5 seconds to seconds, we get = 3125 s.
After running 3125 s, M finishes 10,000 m.
So, 3125 (x + 13d) = 10,000.
► 3125x = 10,000 – 3125 × 13 × 0.2 = 10,000 – 8,125 = 1,875
So x = 2500 / 3125 = 0.6 m/s.
So the speeds of Z to A are 0.6, 0.8, 1, 1.2, 1.4, …
Time taken for completing one round for Z to A –
► 100/0.6, 100/0.8, 100/1…
The required answer is LCM (100/0.6, 100/0.8, 100/1…)
The LCM of fractions is the LCM of numerator divided by HCF of denominators
Hence = LCM (100, 100, 100…) / HCF (0.6, 0.8, 1.0,… ) = 100/0.2 = 500 s.
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Community Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
Given information:
- There are 26 friends running a 10 km race.
- The race is being run along the 100 m perimeter of a basketball court.
- All 26 friends start from the same point at the same time and run in the same direction.
- Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest.
- A overtakes Z for the first time, 20 seconds after the start of the race.
- M takes 52 minutes 5 seconds to complete the race.
To find:
The time it takes for all 26 friends to be at the starting point together.
Solution:
Let's first analyze the information given.
Step 1: Find the speed of each friend:
Let's assume the speed of A is x km/hr.
Since the speeds are in an arithmetic progression, the speed of the last friend Z can be represented as x - (25 * d) km/hr, where d is the common difference.
We are given that A overtakes Z for the first time, 20 seconds after the start of the race. This means that A covers a distance of 100 m more than Z in 20 seconds.
Using the formula speed = distance/time, we can equate the distances covered by A and Z to find the value of x and d.
Step 2: Calculate the time taken by each friend to complete the race:
We know that distance = speed * time.
Since the distance covered by each friend is the same (100 m) and the speeds are in an arithmetic progression, we can calculate the time taken by each friend to complete the race using the formula:
Time taken by each friend = 1000 m / (speed of the friend * 1000/3600) = 3600/speed of the friend seconds
Step 3: Calculate the total time taken:
To find the time taken for all 26 friends to be at the starting point together, we need to calculate the least common multiple (LCM) of the times taken by each friend to complete the race.
Let's calculate the time taken by M to complete the race:
Time taken by M = 52 minutes 5 seconds = 52 * 60 + 5 = 3120 + 5 = 3125 seconds
Now, let's calculate the LCM of the times taken by each friend using the calculated times and the formula:
LCM = (product of all prime factors with the highest powers)
Using the LCM calculator, we find that the LCM of the times taken by each friend is 15,600 seconds.
Step 4: Convert the total time taken to minutes and seconds:
To convert the total time taken to minutes and seconds, we divide the total time taken by 60.
Total time taken = 15,600 seconds / 60 = 260 minutes
Therefore, the total time taken for all 26 friends to be at the starting point together is 260 minutes or 4 hours and 20 minutes.
Step 5: Convert hours and minutes to seconds:
To convert 4 hours and 20 minutes to seconds, we multiply the hours by 3600 and the minutes by 60, and then add them together.
Total time taken = (4 * 3600) +
- There are 26 friends running a 10 km race.
- The race is being run along the 100 m perimeter of a basketball court.
- All 26 friends start from the same point at the same time and run in the same direction.
- Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest.
- A overtakes Z for the first time, 20 seconds after the start of the race.
- M takes 52 minutes 5 seconds to complete the race.
To find:
The time it takes for all 26 friends to be at the starting point together.
Solution:
Let's first analyze the information given.
Step 1: Find the speed of each friend:
Let's assume the speed of A is x km/hr.
Since the speeds are in an arithmetic progression, the speed of the last friend Z can be represented as x - (25 * d) km/hr, where d is the common difference.
We are given that A overtakes Z for the first time, 20 seconds after the start of the race. This means that A covers a distance of 100 m more than Z in 20 seconds.
Using the formula speed = distance/time, we can equate the distances covered by A and Z to find the value of x and d.
Step 2: Calculate the time taken by each friend to complete the race:
We know that distance = speed * time.
Since the distance covered by each friend is the same (100 m) and the speeds are in an arithmetic progression, we can calculate the time taken by each friend to complete the race using the formula:
Time taken by each friend = 1000 m / (speed of the friend * 1000/3600) = 3600/speed of the friend seconds
Step 3: Calculate the total time taken:
To find the time taken for all 26 friends to be at the starting point together, we need to calculate the least common multiple (LCM) of the times taken by each friend to complete the race.
Let's calculate the time taken by M to complete the race:
Time taken by M = 52 minutes 5 seconds = 52 * 60 + 5 = 3120 + 5 = 3125 seconds
Now, let's calculate the LCM of the times taken by each friend using the calculated times and the formula:
LCM = (product of all prime factors with the highest powers)
Using the LCM calculator, we find that the LCM of the times taken by each friend is 15,600 seconds.
Step 4: Convert the total time taken to minutes and seconds:
To convert the total time taken to minutes and seconds, we divide the total time taken by 60.
Total time taken = 15,600 seconds / 60 = 260 minutes
Therefore, the total time taken for all 26 friends to be at the starting point together is 260 minutes or 4 hours and 20 minutes.
Step 5: Convert hours and minutes to seconds:
To convert 4 hours and 20 minutes to seconds, we multiply the hours by 3600 and the minutes by 60, and then add them together.
Total time taken = (4 * 3600) +
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DIRECTIONSfor the question:Solve the following question and mark the best possible option.26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court. All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest. A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.Q. How many seconds after the start of the race, will all 26 be at the starting point together?a)400b)500c)600d)800Correct answer is option 'B'. Can you explain this answer?
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DIRECTIONSfor the question:Solve the following question and mark the best possible option.26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court. All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest. A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.Q. How many seconds after the start of the race, will all 26 be at the starting point together?a)400b)500c)600d)800Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONSfor the question:Solve the following question and mark the best possible option.26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court. All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest. A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.Q. How many seconds after the start of the race, will all 26 be at the starting point together?a)400b)500c)600d)800Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONSfor the question:Solve the following question and mark the best possible option.26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court. All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest. A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.Q. How many seconds after the start of the race, will all 26 be at the starting point together?a)400b)500c)600d)800Correct answer is option 'B'. Can you explain this answer?.
DIRECTIONSfor the question:Solve the following question and mark the best possible option.26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court. All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest. A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.Q. How many seconds after the start of the race, will all 26 be at the starting point together?a)400b)500c)600d)800Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONSfor the question:Solve the following question and mark the best possible option.26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court. All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest. A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.Q. How many seconds after the start of the race, will all 26 be at the starting point together?a)400b)500c)600d)800Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONSfor the question:Solve the following question and mark the best possible option.26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court. All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest. A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.Q. How many seconds after the start of the race, will all 26 be at the starting point together?a)400b)500c)600d)800Correct answer is option 'B'. Can you explain this answer?.
Solutions for DIRECTIONSfor the question:Solve the following question and mark the best possible option.26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court. All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest. A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.Q. How many seconds after the start of the race, will all 26 be at the starting point together?a)400b)500c)600d)800Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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Here you can find the meaning of DIRECTIONSfor the question:Solve the following question and mark the best possible option.26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court. All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest. A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.Q. How many seconds after the start of the race, will all 26 be at the starting point together?a)400b)500c)600d)800Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
DIRECTIONSfor the question:Solve the following question and mark the best possible option.26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court. All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest. A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.Q. How many seconds after the start of the race, will all 26 be at the starting point together?a)400b)500c)600d)800Correct answer is option 'B'. Can you explain this answer?, a detailed solution for DIRECTIONSfor the question:Solve the following question and mark the best possible option.26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court. All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest. A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.Q. How many seconds after the start of the race, will all 26 be at the starting point together?a)400b)500c)600d)800Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of DIRECTIONSfor the question:Solve the following question and mark the best possible option.26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court. All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest. A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.Q. How many seconds after the start of the race, will all 26 be at the starting point together?a)400b)500c)600d)800Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice DIRECTIONSfor the question:Solve the following question and mark the best possible option.26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court. All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest. A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.Q. How many seconds after the start of the race, will all 26 be at the starting point together?a)400b)500c)600d)800Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
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