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A cyclist moves non-stop from A to B, a distance of 14 km, at a certain average speed. If his average speed reduces by 1 km per hour, he takes 20 minutes more to cover the same distance. The original average speed of the cyclist is
- a)5 km/hour
- b)6 km/hour
- c)7 km/hour
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A cyclist moves non-stop from A to B, a distance of 14 km, at a certai...
Let the original average speed be x
∴ Reduced speed = x - 1
∴ Reduced speed = x - 1
Difference in time = Time taken at average speed (x - 1) - Time taken at average speed x
20/60 = 14/(x - 1) - 14/x [∵ Time = Distance/Speed]
1/3 = 14 × [1/(x - 1) - 1/x]
1/3 = 14/[x(x - 1)]
x(x - 1) = 42
x2 - x - 42 = 0
x2 - 7x + 6x - 42 = 0
x(x - 7) + 6(x - 7) = 0
(x + 6) (x - 7) = 0
x cannot be negative
∴ x = 7 km/hr
1/3 = 14 × [1/(x - 1) - 1/x]
1/3 = 14/[x(x - 1)]
x(x - 1) = 42
x2 - x - 42 = 0
x2 - 7x + 6x - 42 = 0
x(x - 7) + 6(x - 7) = 0
(x + 6) (x - 7) = 0
x cannot be negative
∴ x = 7 km/hr
Most Upvoted Answer
A cyclist moves non-stop from A to B, a distance of 14 km, at a certai...
Let's solve the problem step by step:
1. Initial assumptions:
- Distance between points A and B = 14 km
- Initial average speed = x km/hour
- Reduced average speed = (x - 1) km/hour
- Time taken at initial speed = t hours
2. Calculation of time taken at initial speed:
- Using the formula: Time = Distance/Speed
- Time taken at initial speed: t = 14/x
3. Calculation of time taken at reduced speed:
- Time taken at reduced speed: (t + 1/3) hours (20 minutes = 1/3 hour)
- Distance remains the same, so time = Distance/Speed
- Time taken at reduced speed: 14/(x - 1) = t + 1/3
4. Equation setup:
- From step 2 and step 3, we have:
- 14/x = 14/(x - 1) + 1/3
- Simplifying the equation, we get: x^2 - 7x + 14 = 0
- Solving the quadratic equation, we find x = 7 or x = 2 (Rejecting as it is not possible)
5. Conclusion:
- The original average speed of the cyclist is 7 km/hour (option c)
Therefore, the correct answer is option 'c' - 7 km/hour.
1. Initial assumptions:
- Distance between points A and B = 14 km
- Initial average speed = x km/hour
- Reduced average speed = (x - 1) km/hour
- Time taken at initial speed = t hours
2. Calculation of time taken at initial speed:
- Using the formula: Time = Distance/Speed
- Time taken at initial speed: t = 14/x
3. Calculation of time taken at reduced speed:
- Time taken at reduced speed: (t + 1/3) hours (20 minutes = 1/3 hour)
- Distance remains the same, so time = Distance/Speed
- Time taken at reduced speed: 14/(x - 1) = t + 1/3
4. Equation setup:
- From step 2 and step 3, we have:
- 14/x = 14/(x - 1) + 1/3
- Simplifying the equation, we get: x^2 - 7x + 14 = 0
- Solving the quadratic equation, we find x = 7 or x = 2 (Rejecting as it is not possible)
5. Conclusion:
- The original average speed of the cyclist is 7 km/hour (option c)
Therefore, the correct answer is option 'c' - 7 km/hour.
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A cyclist moves non-stop from A to B, a distance of 14 km, at a certain average speed. If his average speed reduces by 1 km per hour, he takes 20 minutes more to cover the same distance. The original average speed of the cyclist isa)5 km/hourb)6 km/hourc)7 km/hourd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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A cyclist moves non-stop from A to B, a distance of 14 km, at a certain average speed. If his average speed reduces by 1 km per hour, he takes 20 minutes more to cover the same distance. The original average speed of the cyclist isa)5 km/hourb)6 km/hourc)7 km/hourd)None of the aboveCorrect answer is option 'C'. 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 A cyclist moves non-stop from A to B, a distance of 14 km, at a certain average speed. If his average speed reduces by 1 km per hour, he takes 20 minutes more to cover the same distance. The original average speed of the cyclist isa)5 km/hourb)6 km/hourc)7 km/hourd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cyclist moves non-stop from A to B, a distance of 14 km, at a certain average speed. If his average speed reduces by 1 km per hour, he takes 20 minutes more to cover the same distance. The original average speed of the cyclist isa)5 km/hourb)6 km/hourc)7 km/hourd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
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