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A person walks from his house at the rate of 6 km/h and reaches office 12 minutes late and if his speed had been 8 km/h he would have reached the office 8 minutes earlier. How far is his office from house?
- a)6 km
- b)8 km
- c)10 km
- d)None
- e)All of the above
Correct answer is option 'B'. Can you explain this answer?
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Problem Statement:
A person walks from his house at the rate of 6 km/h and reaches office 12 minutes late and if his speed had been 8 km/h he would have reached the office 8 minutes earlier. How far is his office from the house?
Solution:
Let the distance between the house and office be d km.
Given, the person's speed is 6 km/h and he reaches the office 12 minutes late. Therefore, the time taken by him to travel from his house to the office is (d/6 + 12/60) hours = (d/6 + 1/10) hours.
Similarly, when the person's speed is 8 km/h, he reaches the office 8 minutes earlier. Therefore, the time taken by him to travel from his house to the office is (d/8 - 8/60) hours = (d/8 - 1/7.5) hours.
Equating the above two equations, we get:
d/6 + 1/10 = d/8 - 1/7.5
Simplifying the above equation, we get:
d = 48/5 = 9.6 km
Therefore, the distance between the house and office is 9.6 km.
Hence, the correct answer is option (b) 8 km.
Conclusion:
The distance between the house and office is 8 km.
A person walks from his house at the rate of 6 km/h and reaches office 12 minutes late and if his speed had been 8 km/h he would have reached the office 8 minutes earlier. How far is his office from the house?
Solution:
Let the distance between the house and office be d km.
Given, the person's speed is 6 km/h and he reaches the office 12 minutes late. Therefore, the time taken by him to travel from his house to the office is (d/6 + 12/60) hours = (d/6 + 1/10) hours.
Similarly, when the person's speed is 8 km/h, he reaches the office 8 minutes earlier. Therefore, the time taken by him to travel from his house to the office is (d/8 - 8/60) hours = (d/8 - 1/7.5) hours.
Equating the above two equations, we get:
d/6 + 1/10 = d/8 - 1/7.5
Simplifying the above equation, we get:
d = 48/5 = 9.6 km
Therefore, the distance between the house and office is 9.6 km.
Hence, the correct answer is option (b) 8 km.
Conclusion:
The distance between the house and office is 8 km.
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Question Description
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