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M and n are 2 points on a straight road Yamuna and Ganga run from m and n respectively towards n and m after crossing each other Yamuna and Ganga reach there respective destinations in 2 minutes and 8 minutes respectively if they start at the same time then the ratio of Yamuna's speed to Ganga's speed is what?
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M and n are 2 points on a straight road Yamuna and Ganga run from m an...
Problem Analysis:
We are given that two points M and N are on a straight road. Yamuna and Ganga start from M and N respectively and move towards each other. After crossing each other, they reach their respective destinations in 2 minutes and 8 minutes respectively. We need to find the ratio of Yamuna's speed to Ganga's speed.
Let's assume:
Let the distance between M and N be D units.
Let the speed of Yamuna be x units/minute.
Let the speed of Ganga be y units/minute.
Calculating the distances:
When Yamuna and Ganga start from their respective points and move towards each other, they will meet at some point P on the road. Let the distance between M and P be d units. Therefore, the distance between P and N will be (D - d) units.
Since Yamuna and Ganga reach their respective destinations in 2 minutes and 8 minutes respectively, we can write the equation:
d/x + (D - d)/y = 2 (Equation 1)
(D - d)/x + d/y = 8 (Equation 2)
Simplifying Equation 1, we get:
d/y + (D - d)/y = 2x
(D - d)/y = 2x - d/y
Substituting this value in Equation 2, we get:
(D - d)/x + 2x - d/y = 8
Simplifying further, we get:
(D - d)/x + d/y = 8 - 2x
We can further simplify this equation as:
D/x - d/x + d/y = 8 - 2x
D/x + d/y = 8 - 2x + d/x
Solving the equations:
From Equation 1, we have:
d/x + (D - d)/y = 2
Multiplying both sides by xy, we get:
yd + x(D - d) = 2xy
Expanding and rearranging, we get:
yd + xD - xd = 2xy
yd - xd = 2xy - xD
d(y - x) = x(2y - D)
d = x(2y - D)/(y - x)
Substituting this value of d in the equation D/x + d/y = 8 - 2x + d/x, we get:
D/x + x(2y - D)/(y - x)y = 8 - 2x + x(2y - D)/x
Simplifying, we get:
D/x + 2y - D/y = 8 - 2x + 2y - D/x
Further simplifying, we get:
D/x - D/y = 8 - 2x - D/x
D/x - D/y - D/x = 8 - 2x
-D/y = 8 - 2x
D/y = 2x - 8
D/y = 2(x - 4)
Conclusion:
From the above equation, we can see that the ratio of D/y to x - 4 is 2. Therefore, the ratio of Yamuna's speed to Ganga's speed is 2.
We are given that two points M and N are on a straight road. Yamuna and Ganga start from M and N respectively and move towards each other. After crossing each other, they reach their respective destinations in 2 minutes and 8 minutes respectively. We need to find the ratio of Yamuna's speed to Ganga's speed.
Let's assume:
Let the distance between M and N be D units.
Let the speed of Yamuna be x units/minute.
Let the speed of Ganga be y units/minute.
Calculating the distances:
When Yamuna and Ganga start from their respective points and move towards each other, they will meet at some point P on the road. Let the distance between M and P be d units. Therefore, the distance between P and N will be (D - d) units.
Since Yamuna and Ganga reach their respective destinations in 2 minutes and 8 minutes respectively, we can write the equation:
d/x + (D - d)/y = 2 (Equation 1)
(D - d)/x + d/y = 8 (Equation 2)
Simplifying Equation 1, we get:
d/y + (D - d)/y = 2x
(D - d)/y = 2x - d/y
Substituting this value in Equation 2, we get:
(D - d)/x + 2x - d/y = 8
Simplifying further, we get:
(D - d)/x + d/y = 8 - 2x
We can further simplify this equation as:
D/x - d/x + d/y = 8 - 2x
D/x + d/y = 8 - 2x + d/x
Solving the equations:
From Equation 1, we have:
d/x + (D - d)/y = 2
Multiplying both sides by xy, we get:
yd + x(D - d) = 2xy
Expanding and rearranging, we get:
yd + xD - xd = 2xy
yd - xd = 2xy - xD
d(y - x) = x(2y - D)
d = x(2y - D)/(y - x)
Substituting this value of d in the equation D/x + d/y = 8 - 2x + d/x, we get:
D/x + x(2y - D)/(y - x)y = 8 - 2x + x(2y - D)/x
Simplifying, we get:
D/x + 2y - D/y = 8 - 2x + 2y - D/x
Further simplifying, we get:
D/x - D/y = 8 - 2x - D/x
D/x - D/y - D/x = 8 - 2x
-D/y = 8 - 2x
D/y = 2x - 8
D/y = 2(x - 4)
Conclusion:
From the above equation, we can see that the ratio of D/y to x - 4 is 2. Therefore, the ratio of Yamuna's speed to Ganga's speed is 2.
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M and n are 2 points on a straight road Yamuna and Ganga run from m and n respectively towards n and m after crossing each other Yamuna and Ganga reach there respective destinations in 2 minutes and 8 minutes respectively if they start at the same time then the ratio of Yamuna's speed to Ganga's speed is what?
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M and n are 2 points on a straight road Yamuna and Ganga run from m and n respectively towards n and m after crossing each other Yamuna and Ganga reach there respective destinations in 2 minutes and 8 minutes respectively if they start at the same time then the ratio of Yamuna's speed to Ganga's speed is what? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about M and n are 2 points on a straight road Yamuna and Ganga run from m and n respectively towards n and m after crossing each other Yamuna and Ganga reach there respective destinations in 2 minutes and 8 minutes respectively if they start at the same time then the ratio of Yamuna's speed to Ganga's speed is what? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for M and n are 2 points on a straight road Yamuna and Ganga run from m and n respectively towards n and m after crossing each other Yamuna and Ganga reach there respective destinations in 2 minutes and 8 minutes respectively if they start at the same time then the ratio of Yamuna's speed to Ganga's speed is what?.
M and n are 2 points on a straight road Yamuna and Ganga run from m and n respectively towards n and m after crossing each other Yamuna and Ganga reach there respective destinations in 2 minutes and 8 minutes respectively if they start at the same time then the ratio of Yamuna's speed to Ganga's speed is what? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about M and n are 2 points on a straight road Yamuna and Ganga run from m and n respectively towards n and m after crossing each other Yamuna and Ganga reach there respective destinations in 2 minutes and 8 minutes respectively if they start at the same time then the ratio of Yamuna's speed to Ganga's speed is what? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for M and n are 2 points on a straight road Yamuna and Ganga run from m and n respectively towards n and m after crossing each other Yamuna and Ganga reach there respective destinations in 2 minutes and 8 minutes respectively if they start at the same time then the ratio of Yamuna's speed to Ganga's speed is what?.
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