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Ram and Gopi run towards each other starting from k and L respectively with respective speeds of 2 kmph and 3 kmph. After meeting each other, to reach L, if Ram takes 7 hours less than the square of magnitude of the time(in hours) taken by Gopi to reach K, find the distance between K and L? A) 25km B) 28km C) 30 km d) 32 km The correct answer is option C) 30 km, can anyone explain?
Verified Answer
Ram and Gopi run towards each other starting from k and L respectively...
Let M be the Meeting Point of Ram and Gopi.
Let KM = x and ML = y.
Let the time taken to meet be 't' hours.
Therefore,
Distance traveled by Ram in time t = KM = x = 2t km
Distance traveled by Gopi in time t = ML = y = 3t km
Hence, x/y = 2/3
Hence, Let x = 2k and y = 3k.
After meeting at time t,
let tR be the time taken by Ram to reach L, and let tG be the time taken by Gopi to reach K
tR = Distance traveled by Ram / Speed of Ram = y/2
tG = Distance traveled by Gopi / Speed of Gopi = x/3
From "to reach L, if Ram takes 7 hours less than the square of the magnitude of the time (in hours) taken by Gopi to reach K",
tR = (tG)^2 − 7
=> y/2 = (x/3)^2 − 7
=> (2x)^2 − 9y − 126 = 0
Substituting for x and y as 2k and 3k,
=> (2k)^2 − 9(3k) − 126 = 0
=> 4 k^2 − 27k − 126 = 0
Solving for k,
=> k = 6 OR k = −(21/8)
Therefore,
x = 2k = 12
y = 3k = 18
Distance between K & L,
KL = x + y = 30 kms
Therefore the distance between K & L is 30 kms.
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Most Upvoted Answer
Ram and Gopi run towards each other starting from k and L respectively...
Given:
- The speed of Ram is 2 kmph.
- The speed of Gopi is 3 kmph.
To find:
The distance between points K and L.
Approach:
Let's assume that the distance between K and L is 'd' km.
1. Meeting Point:
- Since Ram and Gopi start at different points and run towards each other, they will meet at some point between K and L.
- Let's assume they meet at point M.
- The distance covered by Ram from K to M is 'x' km.
- The distance covered by Gopi from L to M is 'd - x' km.
2. Time taken to meet:
- The time taken by Ram to cover the distance 'x' is given by t1 = x/2 hours.
- The time taken by Gopi to cover the distance 'd - x' is given by t2 = (d - x)/3 hours.
3. Time taken by Ram to reach L:
- After meeting at point M, Ram has to cover the remaining distance from M to L, which is 'd - x' km.
- The time taken by Ram to cover this distance is given by t3 = (d - x)/2 hours.
4. Time taken by Gopi to reach K:
- After meeting at point M, Gopi has to cover the remaining distance from M to K, which is 'x' km.
- The time taken by Gopi to cover this distance is given by t4 = x/3 hours.
5. Given condition:
- Ram takes 7 hours less than the square of the magnitude of the time taken by Gopi to reach K.
- Mathematically, t3 = t4^2 - 7.
Now, let's solve the equations to find the distance 'd':
- From equation (3), we have t3 = (d - x)/2.
- From equation (4), we have t4 = x/3.
- Substituting the values of t3 and t4 in equation (5), we get (d - x)/2 = (x/3)^2 - 7.
Simplifying the equation:
- (d - x)/2 = x^2/9 - 7.
- 9(d - x) = 2x^2 - 63.
- 9d - 9x = 2x^2 - 63.
- 2x^2 + 9x - 9d + 63 = 0.
Now, to find the value of 'x', we can use the quadratic formula:
- x = (-9 ± √(9^2 - 4(2)(-9d + 63)))/(2(2)).
- x = (-9 ± √(81 + 72d - 504))/(4).
- x = (-9 ± √(72d - 423))/(4).
Since 'x' represents the distance covered by Ram from K to M, it cannot be negative. Therefore, we take the positive value:
- x = (-9 + √(72d - 423))/(4).
Now, substituting the value of 'x' in equation (5), we get:
- (d - (-9 + √(72d - 423))/(4))/2 = ((-9 + √(72d -
- The speed of Ram is 2 kmph.
- The speed of Gopi is 3 kmph.
To find:
The distance between points K and L.
Approach:
Let's assume that the distance between K and L is 'd' km.
1. Meeting Point:
- Since Ram and Gopi start at different points and run towards each other, they will meet at some point between K and L.
- Let's assume they meet at point M.
- The distance covered by Ram from K to M is 'x' km.
- The distance covered by Gopi from L to M is 'd - x' km.
2. Time taken to meet:
- The time taken by Ram to cover the distance 'x' is given by t1 = x/2 hours.
- The time taken by Gopi to cover the distance 'd - x' is given by t2 = (d - x)/3 hours.
3. Time taken by Ram to reach L:
- After meeting at point M, Ram has to cover the remaining distance from M to L, which is 'd - x' km.
- The time taken by Ram to cover this distance is given by t3 = (d - x)/2 hours.
4. Time taken by Gopi to reach K:
- After meeting at point M, Gopi has to cover the remaining distance from M to K, which is 'x' km.
- The time taken by Gopi to cover this distance is given by t4 = x/3 hours.
5. Given condition:
- Ram takes 7 hours less than the square of the magnitude of the time taken by Gopi to reach K.
- Mathematically, t3 = t4^2 - 7.
Now, let's solve the equations to find the distance 'd':
- From equation (3), we have t3 = (d - x)/2.
- From equation (4), we have t4 = x/3.
- Substituting the values of t3 and t4 in equation (5), we get (d - x)/2 = (x/3)^2 - 7.
Simplifying the equation:
- (d - x)/2 = x^2/9 - 7.
- 9(d - x) = 2x^2 - 63.
- 9d - 9x = 2x^2 - 63.
- 2x^2 + 9x - 9d + 63 = 0.
Now, to find the value of 'x', we can use the quadratic formula:
- x = (-9 ± √(9^2 - 4(2)(-9d + 63)))/(2(2)).
- x = (-9 ± √(81 + 72d - 504))/(4).
- x = (-9 ± √(72d - 423))/(4).
Since 'x' represents the distance covered by Ram from K to M, it cannot be negative. Therefore, we take the positive value:
- x = (-9 + √(72d - 423))/(4).
Now, substituting the value of 'x' in equation (5), we get:
- (d - (-9 + √(72d - 423))/(4))/2 = ((-9 + √(72d -
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Ram and Gopi run towards each other starting from k and L respectively with respective speeds of 2 kmph and 3 kmph. After meeting each other, to reach L, if Ram takes 7 hours less than the square of magnitude of the time(in hours) taken by Gopi to reach K, find the distance between K and L? A) 25km B) 28km C) 30 km d) 32 km The correct answer is option C) 30 km, can anyone explain?
Question Description
Ram and Gopi run towards each other starting from k and L respectively with respective speeds of 2 kmph and 3 kmph. After meeting each other, to reach L, if Ram takes 7 hours less than the square of magnitude of the time(in hours) taken by Gopi to reach K, find the distance between K and L? A) 25km B) 28km C) 30 km d) 32 km The correct answer is option C) 30 km, can anyone explain? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Ram and Gopi run towards each other starting from k and L respectively with respective speeds of 2 kmph and 3 kmph. After meeting each other, to reach L, if Ram takes 7 hours less than the square of magnitude of the time(in hours) taken by Gopi to reach K, find the distance between K and L? A) 25km B) 28km C) 30 km d) 32 km The correct answer is option C) 30 km, can anyone explain? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ram and Gopi run towards each other starting from k and L respectively with respective speeds of 2 kmph and 3 kmph. After meeting each other, to reach L, if Ram takes 7 hours less than the square of magnitude of the time(in hours) taken by Gopi to reach K, find the distance between K and L? A) 25km B) 28km C) 30 km d) 32 km The correct answer is option C) 30 km, can anyone explain?.
Ram and Gopi run towards each other starting from k and L respectively with respective speeds of 2 kmph and 3 kmph. After meeting each other, to reach L, if Ram takes 7 hours less than the square of magnitude of the time(in hours) taken by Gopi to reach K, find the distance between K and L? A) 25km B) 28km C) 30 km d) 32 km The correct answer is option C) 30 km, can anyone explain? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Ram and Gopi run towards each other starting from k and L respectively with respective speeds of 2 kmph and 3 kmph. After meeting each other, to reach L, if Ram takes 7 hours less than the square of magnitude of the time(in hours) taken by Gopi to reach K, find the distance between K and L? A) 25km B) 28km C) 30 km d) 32 km The correct answer is option C) 30 km, can anyone explain? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ram and Gopi run towards each other starting from k and L respectively with respective speeds of 2 kmph and 3 kmph. After meeting each other, to reach L, if Ram takes 7 hours less than the square of magnitude of the time(in hours) taken by Gopi to reach K, find the distance between K and L? A) 25km B) 28km C) 30 km d) 32 km The correct answer is option C) 30 km, can anyone explain?.
Solutions for Ram and Gopi run towards each other starting from k and L respectively with respective speeds of 2 kmph and 3 kmph. After meeting each other, to reach L, if Ram takes 7 hours less than the square of magnitude of the time(in hours) taken by Gopi to reach K, find the distance between K and L? A) 25km B) 28km C) 30 km d) 32 km The correct answer is option C) 30 km, can anyone explain? in English & in Hindi are available as part of our courses for CAT.
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