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Two Cars started at same time, same place and towards same direction. First Car goes at uniform speed of 12Km/hr. Second Car goes at speed of 4 Km/hr in first hour and increases it speed by 1 Km/hr for every hour. Then what is the distance traveled by car B when the both the Cars meet for the first time?
- a)196 Km
- b)198 Km
- c)200 Km
- d)204 Km
- e)None
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Two Cars started at same time, same place and towards same direction. ...
12*x = x/2(2*4+(x-1)*1)
X= 17
D = 17*12 =204
X= 17
D = 17*12 =204
Most Upvoted Answer
Two Cars started at same time, same place and towards same direction. ...
Approach:
Let us assume that both the cars meet after ‘t’ hours. Then, the distance traveled by Car A and Car B will be:
Distance traveled by Car A = 12t
Distance traveled by Car B = 4 + 5 + 6 + ….. (n terms)
where n is the number of hours taken by Car B to meet Car A.
We need to find the value of ‘n’ and then calculate the distance traveled by Car B.
Calculation:
Let us assume that both the cars meet after ‘t’ hours.
Distance traveled by Car A = Distance traveled by Car B
12t = 4 + 5 + 6 + ….. (n terms)
We know that the sum of first ‘n’ natural numbers is given by:
1 + 2 + 3 + …. + n = n(n+1)/2
So, the sum of first ‘n-3’ natural numbers will be:
4 + 5 + 6 + …. + (n-3) = (n-3)(n-2)/2
Substituting this value in the above equation, we get:
12t = (n-3)(n-2)/2
24t = n^2 - 5n + 6
n^2 - 5n + 6 - 24t = 0
On solving this quadratic equation, we get:
n = (5 + √(25 - 4(6 - 24t)))/2
n = (5 + √(97 + 96t))/2
n = 4, when t = 2
We know that Car A and Car B meet for the first time after 2 hours.
So, the distance traveled by Car A in 2 hours = 12 × 2 = 24 Km
Distance traveled by Car B in 2 hours = 4 + 5 = 9 Km
Therefore, the distance traveled by Car B when the both the Cars meet for the first time = 24 + 9 = 33 Km
Similarly, we can calculate the distance traveled by Car B for other values of ‘t’ and add them to get the total distance traveled by Car B.
Let us assume that both the cars meet after ‘t’ hours. Then, the distance traveled by Car A and Car B will be:
Distance traveled by Car A = 12t
Distance traveled by Car B = 4 + 5 + 6 + ….. (n terms)
where n is the number of hours taken by Car B to meet Car A.
We need to find the value of ‘n’ and then calculate the distance traveled by Car B.
Calculation:
Let us assume that both the cars meet after ‘t’ hours.
Distance traveled by Car A = Distance traveled by Car B
12t = 4 + 5 + 6 + ….. (n terms)
We know that the sum of first ‘n’ natural numbers is given by:
1 + 2 + 3 + …. + n = n(n+1)/2
So, the sum of first ‘n-3’ natural numbers will be:
4 + 5 + 6 + …. + (n-3) = (n-3)(n-2)/2
Substituting this value in the above equation, we get:
12t = (n-3)(n-2)/2
24t = n^2 - 5n + 6
n^2 - 5n + 6 - 24t = 0
On solving this quadratic equation, we get:
n = (5 + √(25 - 4(6 - 24t)))/2
n = (5 + √(97 + 96t))/2
n = 4, when t = 2
We know that Car A and Car B meet for the first time after 2 hours.
So, the distance traveled by Car A in 2 hours = 12 × 2 = 24 Km
Distance traveled by Car B in 2 hours = 4 + 5 = 9 Km
Therefore, the distance traveled by Car B when the both the Cars meet for the first time = 24 + 9 = 33 Km
Similarly, we can calculate the distance traveled by Car B for other values of ‘t’ and add them to get the total distance traveled by Car B.
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Two Cars started at same time, same place and towards same direction. First Car goes at uniform speed of 12Km/hr. Second Car goes at speed of 4 Km/hr in first hour and increases it speed by 1 Km/hr for every hour. Then what is the distance traveled by car B when the both the Cars meet for the first time?a)196 Kmb)198 Kmc)200 Kmd)204 Kme)NoneCorrect answer is option 'D'. Can you explain this answer?
Question Description
Two Cars started at same time, same place and towards same direction. First Car goes at uniform speed of 12Km/hr. Second Car goes at speed of 4 Km/hr in first hour and increases it speed by 1 Km/hr for every hour. Then what is the distance traveled by car B when the both the Cars meet for the first time?a)196 Kmb)198 Kmc)200 Kmd)204 Kme)NoneCorrect 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 started at same time, same place and towards same direction. First Car goes at uniform speed of 12Km/hr. Second Car goes at speed of 4 Km/hr in first hour and increases it speed by 1 Km/hr for every hour. Then what is the distance traveled by car B when the both the Cars meet for the first time?a)196 Kmb)198 Kmc)200 Kmd)204 Kme)NoneCorrect 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 started at same time, same place and towards same direction. First Car goes at uniform speed of 12Km/hr. Second Car goes at speed of 4 Km/hr in first hour and increases it speed by 1 Km/hr for every hour. Then what is the distance traveled by car B when the both the Cars meet for the first time?a)196 Kmb)198 Kmc)200 Kmd)204 Kme)NoneCorrect answer is option 'D'. Can you explain this answer?.
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