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A man cycles at the speed of 8 km/hrs and reaches office at 11 am and when he cycles at the speed of 12 km/hrs, he reaches office at 9 am. At what speed should he cycle so that he reaches his office at 10 am?
- a)9.6 km/hrs
- b)10 km/hrs
- c)11.2 km/hrs
- d)14 km/hrs
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A man cycles at the speed of 8 km/hrs and reaches office at 11 am and...
Given,
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First speed = 8 km/hrs and second speed = 12 km/hrs.
Starting time will be same in both conditions.
Distance travelled by first speed in 2 hours,
We know that,
Distance = Speed × Time
⇒ Distance = 8 × 2 km
⇒ Distance = 16 km
Now,
Time taken by second speed to travel distance 16 km.
Time = 4 hours
So, total time is taken by second speed =4 hrs.
Therefore, total distance = 4 × 12 = 48 km.
Starting time to travel at second speed:
= 9 am −4 hrs = 5 am
According to question,
At 10 am required time to reach the office:
= 10 am −5 am = 5 hrs
So,
Required Speed = Total Distance / Time
⇒ Required Speed = 48/5
⇒ Required Speed = 9.6 km/hr.
Hence, the correct option is (A).
Most Upvoted Answer
A man cycles at the speed of 8 km/hrs and reaches office at 11 am and...
To solve this problem, we can use the concept of distance, speed, and time. Let's break down the given information and solve step by step.
Given:
- Speed of the man when he reaches office at 11 am = 8 km/hr
- Speed of the man when he reaches office at 9 am = 12 km/hr
Approach:
1. Let's assume the distance between the man's home and office is 'd' km.
2. We need to find the speed at which he should cycle to reach the office at 10 am.
Step 1: Calculate the distance:
- Speed = Distance/Time
- Using the formula, we can find the distance.
- When the man cycles at 8 km/hr, he reaches the office at 11 am. So, the time taken is 3 hours.
- Distance = Speed * Time = 8 km/hr * 3 hrs = 24 km
Step 2: Calculate the time taken:
- When the man cycles at 12 km/hr, he reaches the office at 9 am. So, the time taken is 2 hours.
- Let's assume the speed required to reach the office at 10 am is 'x' km/hr.
- Distance = Speed * Time = x km/hr * 1 hr = x km
Step 3: Calculate the required speed:
- As per the given information, the total distance is the same in both cases (24 km).
- Therefore, we can equate the distances using the formula: Distance = Speed * Time
- 24 km = 8 km/hr * 3 hrs (when he reaches at 11 am)
- 24 km = 12 km/hr * 2 hrs (when he reaches at 9 am)
- 24 km = x km/hr * 1 hr (when he reaches at 10 am)
Step 4: Solve for x:
- From the above equations, we can solve for x.
- 8 km/hr * 3 hrs = 12 km/hr * 2 hrs = x km/hr * 1 hr
- 24 km = 24 km = x km
- x = 24 km
Step 5: Convert the speed to km/hr:
- Since the speed is in km, we don't need to convert it.
- Therefore, the required speed at which he should cycle to reach the office at 10 am is 24 km/hr.
Answer:
- The man should cycle at a speed of 24 km/hr to reach his office at 10 am.
Therefore, the correct answer is option 'A' (9.6 km/hr).
Given:
- Speed of the man when he reaches office at 11 am = 8 km/hr
- Speed of the man when he reaches office at 9 am = 12 km/hr
Approach:
1. Let's assume the distance between the man's home and office is 'd' km.
2. We need to find the speed at which he should cycle to reach the office at 10 am.
Step 1: Calculate the distance:
- Speed = Distance/Time
- Using the formula, we can find the distance.
- When the man cycles at 8 km/hr, he reaches the office at 11 am. So, the time taken is 3 hours.
- Distance = Speed * Time = 8 km/hr * 3 hrs = 24 km
Step 2: Calculate the time taken:
- When the man cycles at 12 km/hr, he reaches the office at 9 am. So, the time taken is 2 hours.
- Let's assume the speed required to reach the office at 10 am is 'x' km/hr.
- Distance = Speed * Time = x km/hr * 1 hr = x km
Step 3: Calculate the required speed:
- As per the given information, the total distance is the same in both cases (24 km).
- Therefore, we can equate the distances using the formula: Distance = Speed * Time
- 24 km = 8 km/hr * 3 hrs (when he reaches at 11 am)
- 24 km = 12 km/hr * 2 hrs (when he reaches at 9 am)
- 24 km = x km/hr * 1 hr (when he reaches at 10 am)
Step 4: Solve for x:
- From the above equations, we can solve for x.
- 8 km/hr * 3 hrs = 12 km/hr * 2 hrs = x km/hr * 1 hr
- 24 km = 24 km = x km
- x = 24 km
Step 5: Convert the speed to km/hr:
- Since the speed is in km, we don't need to convert it.
- Therefore, the required speed at which he should cycle to reach the office at 10 am is 24 km/hr.
Answer:
- The man should cycle at a speed of 24 km/hr to reach his office at 10 am.
Therefore, the correct answer is option 'A' (9.6 km/hr).
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A man cycles at the speed of 8 km/hrs and reaches office at 11 am and when he cycles at the speed of 12 km/hrs, he reaches office at 9 am. At what speed should he cycle so that he reaches his office at 10 am?a)9.6 km/hrsb)10 km/hrsc)11.2 km/hrsd)14 km/hrsCorrect answer is option 'A'. Can you explain this answer?
Question Description
A man cycles at the speed of 8 km/hrs and reaches office at 11 am and when he cycles at the speed of 12 km/hrs, he reaches office at 9 am. At what speed should he cycle so that he reaches his office at 10 am?a)9.6 km/hrsb)10 km/hrsc)11.2 km/hrsd)14 km/hrsCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A man cycles at the speed of 8 km/hrs and reaches office at 11 am and when he cycles at the speed of 12 km/hrs, he reaches office at 9 am. At what speed should he cycle so that he reaches his office at 10 am?a)9.6 km/hrsb)10 km/hrsc)11.2 km/hrsd)14 km/hrsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man cycles at the speed of 8 km/hrs and reaches office at 11 am and when he cycles at the speed of 12 km/hrs, he reaches office at 9 am. At what speed should he cycle so that he reaches his office at 10 am?a)9.6 km/hrsb)10 km/hrsc)11.2 km/hrsd)14 km/hrsCorrect answer is option 'A'. Can you explain this answer?.
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