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Amitabh covered a distance of 96 km two hours faster than he had planned to. This he achieved by travelling 1 km more every hour than he intended to cover every 1 hour 15 minutes. What was the speed at which Amitabh travelled during the journey?
- a)16 km/h
- b)26 km/h
- c)36 km/h
- d)30 km/h
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Amitabh covered a distance of 96 km two hours faster than he had plann...
In 1 hours 15 minutes an individual will be able to cover 25% more than his speed per hour.
The relationship between the original speed and the new speed is best represented as below:
Original speed
speed per 75 minutes 
New speed.
Thus, to go from the new speed to the original speed the process would be:
New speed
Speed per 75 minutes 
We need to use this process to check the option.
Only the first option satisfies this condition. (at 16 kmph it would take 6 hours while at 12 kmph it would take 8 hours).
The relationship between the original speed and the new speed is best represented as below:
Original speed
speed per 75 minutes New speed.Thus, to go from the new speed to the original speed the process would be:
New speed
Speed per 75 minutes We need to use this process to check the option.Only the first option satisfies this condition. (at 16 kmph it would take 6 hours while at 12 kmph it would take 8 hours).
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Community Answer
Amitabh covered a distance of 96 km two hours faster than he had plann...
Let's break down the information given in the question:
- Amitabh covered a distance of 96 km.
- He covered this distance two hours faster than he had planned to.
- He achieved this by traveling 1 km more every hour than he intended to cover every 1 hour 15 minutes.
Let's calculate Amitabh's planned speed and actual speed and then find the difference to determine his actual speed.
Calculating Planned Speed:
- Let's assume Amitabh planned to cover the distance in 'x' hours.
- Therefore, his planned speed would be 96 km / x hours.
Calculating Actual Speed:
- Amitabh covered the distance 2 hours faster than planned. So, he completed the journey in (x - 2) hours.
- He traveled 1 km more every hour than he intended to cover every 1 hour 15 minutes. In other words, he traveled 1 km more every (1 hour 15 minutes) / 60 minutes = (4/5) hours.
- Therefore, his actual speed would be 96 km / (x - 2) hours + 1 km / (4/5) hours.
Finding the Difference:
- The difference between the planned speed and actual speed is:
Actual Speed - Planned Speed = 96 km / (x - 2) hours + 1 km / (4/5) hours - 96 km / x hours.
According to the question, this difference is equal to 0 because Amitabh covered the distance in the same time he had planned to. So, we can set up the equation:
96 km / (x - 2) hours + 1 km / (4/5) hours - 96 km / x hours = 0.
Simplifying the Equation:
- Multiplying through by x(x - 2)(4/5) to get rid of the denominators:
96 * x * (4/5) + 1 * x(x - 2) - 96 * (x - 2) = 0.
Simplifying further:
(384/5)x + x^2 - 2x - 96x + 192 = 0.
(384/5)x + x^2 - 98x + 192 = 0.
Solving the Quadratic Equation:
- Rearranging the equation:
x^2 - (384/5)x + 98x - 192 = 0.
x^2 - (384/5)x + 98x - 192 = 0.
x^2 - (192/5)x + 98x - 96x - 192 = 0.
x(x - (192/5)) + 96(x - 2) = 0.
(x - 2)(x - 96) = 0.
So, x = 2 or x = 96.
Since Amitabh covered the distance two hours faster than planned, x cannot be 2. Therefore, x = 96.
Calculating Amitabh's Speed:
- Amitabh's planned speed = 96 km / 96 hours = 1 km/hour.
- Amitabh's actual speed = 96 km / (96 - 2) hours + 1 km / (4/5) hours = 16 km/hour.
Therefore, the speed at which Amitabh traveled during the journey was 16 km/hour, which
- Amitabh covered a distance of 96 km.
- He covered this distance two hours faster than he had planned to.
- He achieved this by traveling 1 km more every hour than he intended to cover every 1 hour 15 minutes.
Let's calculate Amitabh's planned speed and actual speed and then find the difference to determine his actual speed.
Calculating Planned Speed:
- Let's assume Amitabh planned to cover the distance in 'x' hours.
- Therefore, his planned speed would be 96 km / x hours.
Calculating Actual Speed:
- Amitabh covered the distance 2 hours faster than planned. So, he completed the journey in (x - 2) hours.
- He traveled 1 km more every hour than he intended to cover every 1 hour 15 minutes. In other words, he traveled 1 km more every (1 hour 15 minutes) / 60 minutes = (4/5) hours.
- Therefore, his actual speed would be 96 km / (x - 2) hours + 1 km / (4/5) hours.
Finding the Difference:
- The difference between the planned speed and actual speed is:
Actual Speed - Planned Speed = 96 km / (x - 2) hours + 1 km / (4/5) hours - 96 km / x hours.
According to the question, this difference is equal to 0 because Amitabh covered the distance in the same time he had planned to. So, we can set up the equation:
96 km / (x - 2) hours + 1 km / (4/5) hours - 96 km / x hours = 0.
Simplifying the Equation:
- Multiplying through by x(x - 2)(4/5) to get rid of the denominators:
96 * x * (4/5) + 1 * x(x - 2) - 96 * (x - 2) = 0.
Simplifying further:
(384/5)x + x^2 - 2x - 96x + 192 = 0.
(384/5)x + x^2 - 98x + 192 = 0.
Solving the Quadratic Equation:
- Rearranging the equation:
x^2 - (384/5)x + 98x - 192 = 0.
x^2 - (384/5)x + 98x - 192 = 0.
x^2 - (192/5)x + 98x - 96x - 192 = 0.
x(x - (192/5)) + 96(x - 2) = 0.
(x - 2)(x - 96) = 0.
So, x = 2 or x = 96.
Since Amitabh covered the distance two hours faster than planned, x cannot be 2. Therefore, x = 96.
Calculating Amitabh's Speed:
- Amitabh's planned speed = 96 km / 96 hours = 1 km/hour.
- Amitabh's actual speed = 96 km / (96 - 2) hours + 1 km / (4/5) hours = 16 km/hour.
Therefore, the speed at which Amitabh traveled during the journey was 16 km/hour, which
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