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A cyclist completes a certain journey in 5 hours. He covers half the distance at 16 km./hr. and the second half of the distance at 24 km./hr. The distance (in km) covered by the cyclist is?
- a)96
- b)76
- c)69
- d)82
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A cyclist completes a certain journey in 5 hours. He covers half the d...
Let,
Total distance covered = 2x km
We know that,
Time required = Distance covered/Speed
Given,
Half of the distance i.e. x km is covered at speed 16 km/hr
∴ Time required = x/16 hours
Next half of the distance i.e. x km is covered at speed 24 km/hr
∴ Time required = x/24 hours
Given,
Total time required = 5 hours
∴ x/16 + x/24 = 5
⇒ (3x + 2x)/48 = 5
⇒ 5x = 48 × 5
⇒ x = 48 km
∴ Total distance covered = 2 × 48 km = 96 km
Total distance covered = 2x km
We know that,
Time required = Distance covered/Speed
Given,
Half of the distance i.e. x km is covered at speed 16 km/hr
∴ Time required = x/16 hours
Next half of the distance i.e. x km is covered at speed 24 km/hr
∴ Time required = x/24 hours
Given,
Total time required = 5 hours
∴ x/16 + x/24 = 5
⇒ (3x + 2x)/48 = 5
⇒ 5x = 48 × 5
⇒ x = 48 km
∴ Total distance covered = 2 × 48 km = 96 km
Most Upvoted Answer
A cyclist completes a certain journey in 5 hours. He covers half the d...
Understanding the Journey
The cyclist completes the journey in 5 hours, covering half the distance at different speeds. Let's denote the total distance as D km.
Distance Breakdown
- Half the distance: D/2 km at 16 km/hr
- Second half the distance: D/2 km at 24 km/hr
Calculating Time for Each Half
1. Time for the first half:
- Speed = 16 km/hr
- Distance = D/2 km
- Time = Distance / Speed = (D/2) / 16 = D/32 hours
2. Time for the second half:
- Speed = 24 km/hr
- Distance = D/2 km
- Time = Distance / Speed = (D/2) / 24 = D/48 hours
Total Time Calculation
The total time taken for the journey is the sum of the time for both halves:
Total Time = Time for first half + Time for second half
= D/32 + D/48
To add these fractions, find a common denominator:
- The least common multiple of 32 and 48 is 96.
Finding Common Time
- Convert D/32 to a fraction with a denominator of 96:
D/32 = (3D)/96
- Convert D/48 to a fraction with a denominator of 96:
D/48 = (2D)/96
Now adding these gives:
Total Time = (3D + 2D) / 96 = 5D / 96
Setting Total Time Equal to 5 Hours
Setting this equal to 5 hours:
5D / 96 = 5
To solve for D, multiply both sides by 96:
5D = 480
Then divide by 5:
D = 96 km
Thus, the total distance covered by the cyclist is 96 km, confirming option 'A' as the correct answer.
The cyclist completes the journey in 5 hours, covering half the distance at different speeds. Let's denote the total distance as D km.
Distance Breakdown
- Half the distance: D/2 km at 16 km/hr
- Second half the distance: D/2 km at 24 km/hr
Calculating Time for Each Half
1. Time for the first half:
- Speed = 16 km/hr
- Distance = D/2 km
- Time = Distance / Speed = (D/2) / 16 = D/32 hours
2. Time for the second half:
- Speed = 24 km/hr
- Distance = D/2 km
- Time = Distance / Speed = (D/2) / 24 = D/48 hours
Total Time Calculation
The total time taken for the journey is the sum of the time for both halves:
Total Time = Time for first half + Time for second half
= D/32 + D/48
To add these fractions, find a common denominator:
- The least common multiple of 32 and 48 is 96.
Finding Common Time
- Convert D/32 to a fraction with a denominator of 96:
D/32 = (3D)/96
- Convert D/48 to a fraction with a denominator of 96:
D/48 = (2D)/96
Now adding these gives:
Total Time = (3D + 2D) / 96 = 5D / 96
Setting Total Time Equal to 5 Hours
Setting this equal to 5 hours:
5D / 96 = 5
To solve for D, multiply both sides by 96:
5D = 480
Then divide by 5:
D = 96 km
Thus, the total distance covered by the cyclist is 96 km, confirming option 'A' as the correct answer.
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A cyclist completes a certain journey in 5 hours. He covers half the distance at 16 km./hr. and the second half of the distance at 24 km./hr. The distance (in km) covered by the cyclist is?a)96b)76c)69d)82Correct answer is option 'A'. Can you explain this answer?
Question Description
A cyclist completes a certain journey in 5 hours. He covers half the distance at 16 km./hr. and the second half of the distance at 24 km./hr. The distance (in km) covered by the cyclist is?a)96b)76c)69d)82Correct answer is option 'A'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A cyclist completes a certain journey in 5 hours. He covers half the distance at 16 km./hr. and the second half of the distance at 24 km./hr. The distance (in km) covered by the cyclist is?a)96b)76c)69d)82Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cyclist completes a certain journey in 5 hours. He covers half the distance at 16 km./hr. and the second half of the distance at 24 km./hr. The distance (in km) covered by the cyclist is?a)96b)76c)69d)82Correct answer is option 'A'. Can you explain this answer?.
A cyclist completes a certain journey in 5 hours. He covers half the distance at 16 km./hr. and the second half of the distance at 24 km./hr. The distance (in km) covered by the cyclist is?a)96b)76c)69d)82Correct answer is option 'A'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A cyclist completes a certain journey in 5 hours. He covers half the distance at 16 km./hr. and the second half of the distance at 24 km./hr. The distance (in km) covered by the cyclist is?a)96b)76c)69d)82Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cyclist completes a certain journey in 5 hours. He covers half the distance at 16 km./hr. and the second half of the distance at 24 km./hr. The distance (in km) covered by the cyclist is?a)96b)76c)69d)82Correct answer is option 'A'. Can you explain this answer?.
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