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Two cyclists start simultaneously towards each other from Aurangabad and Ellora, which are 28km apart. An hour later they meet and keep pedalling with the same speed without stopping. Thesecond cyclist arrives at Ellora 35 minutes later than the first arrives at Aurangabad. Find thespeed of the cyclist who started from Ellora.
- a)12 km/h
- b)16 km/h
- c)15 km/h
- d)10 km/h
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Two cyclists start simultaneously towards each other from Aurangabad a...
Since the two motorists meet after an hour, their relative speed is 28 kmph. Use options to check
out the values. Since the speed of the faster cyclist is asked for it has to be greater than 14 kmph.
Hence only check options > 14 kmph.
out the values. Since the speed of the faster cyclist is asked for it has to be greater than 14 kmph.
Hence only check options > 14 kmph.
Most Upvoted Answer
Two cyclists start simultaneously towards each other from Aurangabad a...
Let person A be the one moving from aurangabad and N moving from Ellora
Lets say they meet at a point C which is x km away from aurangabad and (28 - x) km away from Ellora.
The distance covered by A is x Km and by B is (28 - x) km.
This is covered in 1 hrs so the speed for :
A = x km/h
B = (28 - x) km / h
A has (28 - x) km to cover whereas B has x km more to cover.
Since we have the distance and the speeds for the two, we can get the time taken to reach respective destinations.
A : (28 - x) / x
B : x /(28 - x)
We know that A arrives 35 minutes later which is equivalent to 7 / 12 hrs
Putting this in an equation form we have :
x / (28 - x) + 7/12 = (28 - x) / x
Expanding the equation we get :
12 x^2 + 196 x - 7x^2 = 9408 - 672x + 12x^2
Collecting like terms together :
- 7x^2 + 868 x - 9408 = 0
Dividing through by a negative :
7x^2 - 868 x + 9408 = 0
Solving for X using the quadratic formula we have :
X = {868 +/-√(868x - 4 x7 x 9408)} / (2 x 7)
X = {868 +/- (700)} / 14
X = 12 or 112
We pick 12 since 112 is more than the total distance thus it is unrealistic.
Speed of B is : (28 - 12) = 16
16 m / s
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Community Answer
Two cyclists start simultaneously towards each other from Aurangabad a...
Given:
- Distance between Aurangabad and Ellora = 28 km
- Two cyclists start simultaneously towards each other from Aurangabad and Ellora
- An hour later they meet
- Second cyclist arrives at Ellora 35 minutes later than the first arrives at Aurangabad
To find:
- Speed of the cyclist who started from Ellora
Solution:
Let's assume the speed of the cyclist who started from Aurangabad as 'a' km/h and the speed of the cyclist who started from Ellora as 'b' km/h.
- Distance covered by the first cyclist in 1 hour = a x 1 = a km
- Distance covered by the second cyclist in 1 hour = b x 1 = b km
- Total distance covered by both cyclists in 1 hour = a + b km (they meet after 1 hour)
- Remaining distance between them = 28 - (a + b) km
As per the given condition, the first cyclist arrives at Aurangabad 35 minutes before the second cyclist arrives at Ellora. This means, the first cyclist covers the remaining distance in (60 - 35) = 25 minutes = 25/60 hours.
- Distance covered by the first cyclist in 25/60 hours = (a x 25)/60 km
- Distance covered by the second cyclist in 25/60 hours = (b x 25)/60 km
Total distance covered by the first cyclist = a + (a x 25)/60 km
Total distance covered by the second cyclist = b + (b x 25)/60 km
As per the given condition, both cyclists cover the same distance in the same time without stopping. Therefore,
Total distance covered by the first cyclist = Total distance covered by the second cyclist
a + (a x 25)/60 = b + (b x 25)/60
Simplifying the equation, we get:
a + (5a/12) = b + (5b/12)
12a + 5a = 12b + 5b
17a = 17b
a = b
Therefore, the speed of both cyclists is the same. Let's assume it to be 'x' km/h. Then,
2x = 28/(1 + 35/60)
2x = 28/(95/60)
2x = 33.6842
x = 16.8421
Therefore, the speed of the cyclist who started from Ellora is 16 km/h (approx).
Answer: Option (b) 16 km/h
- Distance between Aurangabad and Ellora = 28 km
- Two cyclists start simultaneously towards each other from Aurangabad and Ellora
- An hour later they meet
- Second cyclist arrives at Ellora 35 minutes later than the first arrives at Aurangabad
To find:
- Speed of the cyclist who started from Ellora
Solution:
Let's assume the speed of the cyclist who started from Aurangabad as 'a' km/h and the speed of the cyclist who started from Ellora as 'b' km/h.
- Distance covered by the first cyclist in 1 hour = a x 1 = a km
- Distance covered by the second cyclist in 1 hour = b x 1 = b km
- Total distance covered by both cyclists in 1 hour = a + b km (they meet after 1 hour)
- Remaining distance between them = 28 - (a + b) km
As per the given condition, the first cyclist arrives at Aurangabad 35 minutes before the second cyclist arrives at Ellora. This means, the first cyclist covers the remaining distance in (60 - 35) = 25 minutes = 25/60 hours.
- Distance covered by the first cyclist in 25/60 hours = (a x 25)/60 km
- Distance covered by the second cyclist in 25/60 hours = (b x 25)/60 km
Total distance covered by the first cyclist = a + (a x 25)/60 km
Total distance covered by the second cyclist = b + (b x 25)/60 km
As per the given condition, both cyclists cover the same distance in the same time without stopping. Therefore,
Total distance covered by the first cyclist = Total distance covered by the second cyclist
a + (a x 25)/60 = b + (b x 25)/60
Simplifying the equation, we get:
a + (5a/12) = b + (5b/12)
12a + 5a = 12b + 5b
17a = 17b
a = b
Therefore, the speed of both cyclists is the same. Let's assume it to be 'x' km/h. Then,
2x = 28/(1 + 35/60)
2x = 28/(95/60)
2x = 33.6842
x = 16.8421
Therefore, the speed of the cyclist who started from Ellora is 16 km/h (approx).
Answer: Option (b) 16 km/h
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Two cyclists start simultaneously towards each other from Aurangabad and Ellora, which are 28km apart. An hour later they meet and keep pedalling with the same speed without stopping. Thesecond cyclist arrives at Ellora 35 minutes later than the first arrives at Aurangabad. Find thespeed of the cyclist who started from Ellora.a)12 km/hb)16 km/hc)15 km/hd)10 km/hCorrect answer is option 'B'. Can you explain this answer? for Quant 2026 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Two cyclists start simultaneously towards each other from Aurangabad and Ellora, which are 28km apart. An hour later they meet and keep pedalling with the same speed without stopping. Thesecond cyclist arrives at Ellora 35 minutes later than the first arrives at Aurangabad. Find thespeed of the cyclist who started from Ellora.a)12 km/hb)16 km/hc)15 km/hd)10 km/hCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cyclists start simultaneously towards each other from Aurangabad and Ellora, which are 28km apart. An hour later they meet and keep pedalling with the same speed without stopping. Thesecond cyclist arrives at Ellora 35 minutes later than the first arrives at Aurangabad. Find thespeed of the cyclist who started from Ellora.a)12 km/hb)16 km/hc)15 km/hd)10 km/hCorrect answer is option 'B'. Can you explain this answer?.
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