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Distance between Lucknow and Patna is 300 km. Mayank leaves at a speed of x km/h from Lucknow towards Patna. After three hours Sharat leaves at the speed of (x + 10) km/h from Lucknow towards Patna. If x and the number of hours taken to meet after Sharat starts are integers, how much distance can Mayank cover before they meet?
- a)174 km
- b)60 km
- c)150 km
- d)180 km
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Distance between Lucknow and Patna is 300 km. Mayank leaves at a speed...
One of the ways of solving this question is going through equations. But after a certain stages we will be required to start assuming the values because all the data are not given.
Another way of doing this problem is: Start working by assuming some values. Let us assume the speed of Mayank =10 km/h. In three hours he has covered 30 km. Now Sharat starts with a speed of 20 km/h. He will take 3 hours to meet Mayank. Till that time, the total distance covered by Mayank = 60 km.
Another way of doing this problem is: Start working by assuming some values. Let us assume the speed of Mayank =10 km/h. In three hours he has covered 30 km. Now Sharat starts with a speed of 20 km/h. He will take 3 hours to meet Mayank. Till that time, the total distance covered by Mayank = 60 km.
Most Upvoted Answer
Distance between Lucknow and Patna is 300 km. Mayank leaves at a speed...
Let us assume mayank is travelling with 10km/hr ; distance covered by him in 3hrs is 30kms.
speed of sharat is 20 km/hr .
lcm of their speed is i.e 10 and 20 >30 is 60
hence they will meet after 6hrs mayank has started hence distance covered by mayank in 6hrs is 60km
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Distance between Lucknow and Patna is 300 km. Mayank leaves at a speed...
Given: Distance between Lucknow and Patna = 300 km
Mayank's speed = x km/h
Sharat's speed = (x+10) km/h
Let's assume that both Mayank and Sharat meet at a distance of d km from Lucknow.
After three hours, Mayank would have covered a distance of 3x km (as he travels for 3 hours).
Let's say Sharat takes t hours to meet Mayank after he starts his journey.
Distance covered by Sharat in t hours = t(x+10)
Distance covered by Mayank in t hours = t(x)
Total distance covered by both of them to meet = d
Therefore, we can form an equation based on the above information:
3x + t(x+10) = d ----(1)
Also, we know that the total distance between Lucknow and Patna is 300 km. Therefore, the total time taken by both Mayank and Sharat to meet each other should be:
t + 3 = (300/d) ----(2)
We need to find the distance covered by Mayank before they meet, which is 3x.
To solve this problem, we can use trial and error method by substituting different values of x until we find the one that satisfies both equations (1) and (2).
Let's start with x = 20 km/h
From equation (2), we get:
t + 3 = (300/d)
t = (300/d) - 3
Substituting x = 20 in equation (1), we get:
3(20) + t(30) = d
60 + 30t = d
Substituting the value of t from equation (2) in the above equation, we get:
60 + 30[(300/d) - 3] = d
Simplifying the above equation, we get:
d^2 - 240d - 5400 = 0
Using the quadratic formula, we get:
d = 174 or d = -30
Since distance cannot be negative, we can consider d = 174 km.
Substituting d = 174 km in equation (1), we get:
3x + t(x+10) = 174
3(20) + t(30) = 174
t = 3
Therefore, Mayank covers a distance of 3x = 60 km before they meet.
Hence, the correct answer is option (B).
Mayank's speed = x km/h
Sharat's speed = (x+10) km/h
Let's assume that both Mayank and Sharat meet at a distance of d km from Lucknow.
After three hours, Mayank would have covered a distance of 3x km (as he travels for 3 hours).
Let's say Sharat takes t hours to meet Mayank after he starts his journey.
Distance covered by Sharat in t hours = t(x+10)
Distance covered by Mayank in t hours = t(x)
Total distance covered by both of them to meet = d
Therefore, we can form an equation based on the above information:
3x + t(x+10) = d ----(1)
Also, we know that the total distance between Lucknow and Patna is 300 km. Therefore, the total time taken by both Mayank and Sharat to meet each other should be:
t + 3 = (300/d) ----(2)
We need to find the distance covered by Mayank before they meet, which is 3x.
To solve this problem, we can use trial and error method by substituting different values of x until we find the one that satisfies both equations (1) and (2).
Let's start with x = 20 km/h
From equation (2), we get:
t + 3 = (300/d)
t = (300/d) - 3
Substituting x = 20 in equation (1), we get:
3(20) + t(30) = d
60 + 30t = d
Substituting the value of t from equation (2) in the above equation, we get:
60 + 30[(300/d) - 3] = d
Simplifying the above equation, we get:
d^2 - 240d - 5400 = 0
Using the quadratic formula, we get:
d = 174 or d = -30
Since distance cannot be negative, we can consider d = 174 km.
Substituting d = 174 km in equation (1), we get:
3x + t(x+10) = 174
3(20) + t(30) = 174
t = 3
Therefore, Mayank covers a distance of 3x = 60 km before they meet.
Hence, the correct answer is option (B).
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Distance between Lucknow and Patna is 300 km. Mayank leaves at a speed of x km/h from Lucknow towards Patna. After three hours Sharat leaves at the speed of (x + 10) km/h from Lucknow towards Patna. If x and the number of hours taken to meet after Sharat starts are integers, how much distance can Mayank cover before they meet?a)174 kmb)60 kmc)150 kmd)180 kmCorrect answer is option 'B'. Can you explain this answer?
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Distance between Lucknow and Patna is 300 km. Mayank leaves at a speed of x km/h from Lucknow towards Patna. After three hours Sharat leaves at the speed of (x + 10) km/h from Lucknow towards Patna. If x and the number of hours taken to meet after Sharat starts are integers, how much distance can Mayank cover before they meet?a)174 kmb)60 kmc)150 kmd)180 kmCorrect answer is option 'B'. 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 Distance between Lucknow and Patna is 300 km. Mayank leaves at a speed of x km/h from Lucknow towards Patna. After three hours Sharat leaves at the speed of (x + 10) km/h from Lucknow towards Patna. If x and the number of hours taken to meet after Sharat starts are integers, how much distance can Mayank cover before they meet?a)174 kmb)60 kmc)150 kmd)180 kmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Distance between Lucknow and Patna is 300 km. Mayank leaves at a speed of x km/h from Lucknow towards Patna. After three hours Sharat leaves at the speed of (x + 10) km/h from Lucknow towards Patna. If x and the number of hours taken to meet after Sharat starts are integers, how much distance can Mayank cover before they meet?a)174 kmb)60 kmc)150 kmd)180 kmCorrect answer is option 'B'. Can you explain this answer?.
Distance between Lucknow and Patna is 300 km. Mayank leaves at a speed of x km/h from Lucknow towards Patna. After three hours Sharat leaves at the speed of (x + 10) km/h from Lucknow towards Patna. If x and the number of hours taken to meet after Sharat starts are integers, how much distance can Mayank cover before they meet?a)174 kmb)60 kmc)150 kmd)180 kmCorrect answer is option 'B'. 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 Distance between Lucknow and Patna is 300 km. Mayank leaves at a speed of x km/h from Lucknow towards Patna. After three hours Sharat leaves at the speed of (x + 10) km/h from Lucknow towards Patna. If x and the number of hours taken to meet after Sharat starts are integers, how much distance can Mayank cover before they meet?a)174 kmb)60 kmc)150 kmd)180 kmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Distance between Lucknow and Patna is 300 km. Mayank leaves at a speed of x km/h from Lucknow towards Patna. After three hours Sharat leaves at the speed of (x + 10) km/h from Lucknow towards Patna. If x and the number of hours taken to meet after Sharat starts are integers, how much distance can Mayank cover before they meet?a)174 kmb)60 kmc)150 kmd)180 kmCorrect answer is option 'B'. Can you explain this answer?.
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