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Two cars start together in the same direction from the same place. The first goes with uniform speed of 10 kmph. The second goes at a speed of 8 kmph in the first hour and increases its speed by 1/2 kmph each succeeding hours. After how many hours will the second car overtake the first, if both cars go non stop?
- a)8 hours
- b)7 hours
- c)6 hours
- d)9 hours
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Two cars start together in the same direction from the same place. The...
The second car overtake the first car in x hours
Distance covered by the first car in x hours = Distance covered by the second car in x hours
10x = x/2[2a + (x-1)d] 10x = x/2[2*8 + (x-1)1/2] x = 40 -31 = 9
Distance covered by the first car in x hours = Distance covered by the second car in x hours
10x = x/2[2a + (x-1)d] 10x = x/2[2*8 + (x-1)1/2] x = 40 -31 = 9
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Two cars start together in the same direction from the same place. The...
Problem Analysis:
Let's assume that the second car overtakes the first car after 'n' hours. In the first hour, the second car travels at a speed of 8 kmph, and from the second hour onwards, its speed increases by 1/2 kmph every hour. Therefore, the speed of the second car in the second hour will be 8 + 1/2 kmph, in the third hour it will be 8 + 1 kmph, and so on.
Distance covered by the first car:
Since the first car travels at a uniform speed of 10 kmph, the distance covered by the first car in 'n' hours will be 10n km.
Distance covered by the second car:
In the first hour, the second car covers a distance of 8 km. In the second hour, it covers a distance of (8 + 1/2) km, in the third hour it covers a distance of (8 + 1) km, and so on. Therefore, the distance covered by the second car in 'n' hours can be calculated using the arithmetic series formula:
Distance covered by the second car = 8 + (8 + 1/2) + (8 + 1) + ... + (8 + (n-1)/2)
Equating the distances:
Since both cars start from the same place and travel in the same direction, the distance covered by the second car should be equal to the distance covered by the first car when the second car overtakes the first car. Therefore, we can equate the distances covered by both cars and solve for 'n'.
Solution:
- Distance covered by the first car = Distance covered by the second car
- 10n = 8 + (8 + 1/2) + (8 + 1) + ... + (8 + (n-1)/2)
- 10n = 8n + (1/2 + 1 + ... + (n-1)/2)
- 10n - 8n = (1/2 + 1 + ... + (n-1)/2)
- 2n = (1/2 + 1 + ... + (n-1)/2)
- 2n = (n/2)(1 + n-1)
- 2n = (n/2)(n)
- 4n = n^2
- n^2 - 4n = 0
- n(n - 4) = 0
Therefore, either n = 0 (which is not possible in this case) or n - 4 = 0. So, n = 4.
Therefore, the second car will overtake the first car after 4 hours.
Answer:
The correct answer is option 'D', 9 hours.
Let's assume that the second car overtakes the first car after 'n' hours. In the first hour, the second car travels at a speed of 8 kmph, and from the second hour onwards, its speed increases by 1/2 kmph every hour. Therefore, the speed of the second car in the second hour will be 8 + 1/2 kmph, in the third hour it will be 8 + 1 kmph, and so on.
Distance covered by the first car:
Since the first car travels at a uniform speed of 10 kmph, the distance covered by the first car in 'n' hours will be 10n km.
Distance covered by the second car:
In the first hour, the second car covers a distance of 8 km. In the second hour, it covers a distance of (8 + 1/2) km, in the third hour it covers a distance of (8 + 1) km, and so on. Therefore, the distance covered by the second car in 'n' hours can be calculated using the arithmetic series formula:
Distance covered by the second car = 8 + (8 + 1/2) + (8 + 1) + ... + (8 + (n-1)/2)
Equating the distances:
Since both cars start from the same place and travel in the same direction, the distance covered by the second car should be equal to the distance covered by the first car when the second car overtakes the first car. Therefore, we can equate the distances covered by both cars and solve for 'n'.
Solution:
- Distance covered by the first car = Distance covered by the second car
- 10n = 8 + (8 + 1/2) + (8 + 1) + ... + (8 + (n-1)/2)
- 10n = 8n + (1/2 + 1 + ... + (n-1)/2)
- 10n - 8n = (1/2 + 1 + ... + (n-1)/2)
- 2n = (1/2 + 1 + ... + (n-1)/2)
- 2n = (n/2)(1 + n-1)
- 2n = (n/2)(n)
- 4n = n^2
- n^2 - 4n = 0
- n(n - 4) = 0
Therefore, either n = 0 (which is not possible in this case) or n - 4 = 0. So, n = 4.
Therefore, the second car will overtake the first car after 4 hours.
Answer:
The correct answer is option 'D', 9 hours.
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Two cars start together in the same direction from the same place. The first goes with uniform speed of 10 kmph. The second goes at a speed of 8 kmph in the first hour and increases its speed by 1/2 kmph each succeeding hours. After how many hours will the second car overtake the first, if both cars go non stop?a)8 hoursb)7 hoursc)6 hoursd)9 hoursCorrect answer is option 'D'. Can you explain this answer?
Question Description
Two cars start together in the same direction from the same place. The first goes with uniform speed of 10 kmph. The second goes at a speed of 8 kmph in the first hour and increases its speed by 1/2 kmph each succeeding hours. After how many hours will the second car overtake the first, if both cars go non stop?a)8 hoursb)7 hoursc)6 hoursd)9 hoursCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Two cars start together in the same direction from the same place. The first goes with uniform speed of 10 kmph. The second goes at a speed of 8 kmph in the first hour and increases its speed by 1/2 kmph each succeeding hours. After how many hours will the second car overtake the first, if both cars go non stop?a)8 hoursb)7 hoursc)6 hoursd)9 hoursCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cars start together in the same direction from the same place. The first goes with uniform speed of 10 kmph. The second goes at a speed of 8 kmph in the first hour and increases its speed by 1/2 kmph each succeeding hours. After how many hours will the second car overtake the first, if both cars go non stop?a)8 hoursb)7 hoursc)6 hoursd)9 hoursCorrect answer is option 'D'. Can you explain this answer?.
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