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Amit goes to his office by car at the speed of 80 km/hr and reaches 15 minutes earlier. If he goes at the speed 60 km/hr, he reaches 15 minutes late. What will be the speed (in km/hr) of the car to reach on time?
- a)478/7
- b)476/7
- c)480/7
- d)484/7
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Amit goes to his office by car at the speed of 80 km/hr and reaches 15...
Let the speed to reach on time be s.
Let the distance to office be d.
Time taken by car at 80 km/hr = x = d/s = d/80
Time taken by car at 60 km/hr = y = d/s = d/60
Time taken by car at s km/hr = z = d/s = d/s
Given: x = z – 15/60, y = z + 15/60
⇒ d/80 = d/s – 15/60 = d/s – 1/4 ⇒ d(1/80 – 1/s) = -1/4
⇒ d/60 = d/s + 15/60 = d/s + 1/4 ⇒ d(1/60 – 1/s) = 1/4
Dividing the two equations, we get
(1/80 – 1/s)/(1/60 – 1/s) = -1
⇒ 1/80 – 1/s = 1/s – 1/60
⇒ 2/s = 1/80 + 1/60 = 1/20(1/4 + 1/3) = (1/20)(7/12)
⇒ s = 40 × 12/7 = 480/7 km/h
Most Upvoted Answer
Amit goes to his office by car at the speed of 80 km/hr and reaches 15...
To solve this question, we can use the concept of distance, speed, and time.
Let's assume the distance between Amit's home and office is D km.
Given:
Speed of the car while going to the office = 80 km/hr
Time taken to reach the office at this speed = 15 minutes earlier than usual
Calculating Time taken to reach the office at a speed of 80 km/hr:
Time taken = Distance / Speed
Time taken = D / 80
Since Amit reaches 15 minutes earlier than usual, the time taken is reduced by 15 minutes:
Time taken = D / 80 - 15/60
Time taken = D / 80 - 1/4
Time taken = D / 80 - 20/80
Time taken = (D - 20) / 80
Similarly, let's calculate the time taken to reach the office at a speed of 60 km/hr:
Time taken = D / 60 + 15/60
Time taken = D / 60 + 1/4
Time taken = D / 60 + 15/60
Time taken = (D + 15) / 60
Since Amit reaches 15 minutes late, the time taken is increased by 15 minutes:
Time taken = (D + 15) / 60 + 15/60
Time taken = (D + 15 + 15) / 60
Time taken = (D + 30) / 60
Time taken = (D + 30) / 60
Now, to reach on time, the time taken should be the same while going at the speed of the car. So we can equate the two time expressions:
(D - 20) / 80 = (D + 30) / 60
Cross-multiplying:
60(D - 20) = 80(D + 30)
60D - 1200 = 80D + 2400
20D = 3600
D = 180
Therefore, the distance between Amit's home and office is 180 km.
Now, to find the speed at which Amit should drive to reach on time, we can substitute the distance into one of the time expressions:
Time taken = (D - 20) / 80
Time taken = (180 - 20) / 80
Time taken = 160 / 80
Time taken = 2 hours
To find the speed, we can use the formula:
Speed = Distance / Time
Speed = 180 / 2
Speed = 90 km/hr
Therefore, the speed of the car should be 90 km/hr for Amit to reach the office on time.
The correct answer is option C) 480/7.
Let's assume the distance between Amit's home and office is D km.
Given:
Speed of the car while going to the office = 80 km/hr
Time taken to reach the office at this speed = 15 minutes earlier than usual
Calculating Time taken to reach the office at a speed of 80 km/hr:
Time taken = Distance / Speed
Time taken = D / 80
Since Amit reaches 15 minutes earlier than usual, the time taken is reduced by 15 minutes:
Time taken = D / 80 - 15/60
Time taken = D / 80 - 1/4
Time taken = D / 80 - 20/80
Time taken = (D - 20) / 80
Similarly, let's calculate the time taken to reach the office at a speed of 60 km/hr:
Time taken = D / 60 + 15/60
Time taken = D / 60 + 1/4
Time taken = D / 60 + 15/60
Time taken = (D + 15) / 60
Since Amit reaches 15 minutes late, the time taken is increased by 15 minutes:
Time taken = (D + 15) / 60 + 15/60
Time taken = (D + 15 + 15) / 60
Time taken = (D + 30) / 60
Time taken = (D + 30) / 60
Now, to reach on time, the time taken should be the same while going at the speed of the car. So we can equate the two time expressions:
(D - 20) / 80 = (D + 30) / 60
Cross-multiplying:
60(D - 20) = 80(D + 30)
60D - 1200 = 80D + 2400
20D = 3600
D = 180
Therefore, the distance between Amit's home and office is 180 km.
Now, to find the speed at which Amit should drive to reach on time, we can substitute the distance into one of the time expressions:
Time taken = (D - 20) / 80
Time taken = (180 - 20) / 80
Time taken = 160 / 80
Time taken = 2 hours
To find the speed, we can use the formula:
Speed = Distance / Time
Speed = 180 / 2
Speed = 90 km/hr
Therefore, the speed of the car should be 90 km/hr for Amit to reach the office on time.
The correct answer is option C) 480/7.
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Amit goes to his office by car at the speed of 80 km/hr and reaches 15 minutes earlier. If he goes at the speed 60 km/hr, he reaches 15 minutes late. What will be the speed (in km/hr) of the car to reach on time?a)478/7b)476/7c)480/7d)484/7Correct answer is option 'C'. Can you explain this answer?
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