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A boat goes 8 km upstream and 12 km downstream in 7 hours. It goes 9 km upstream and 18 km downstream in 9 hours. What is the speed (in km/h) of the boat in still water?
- a)5
- b)4
- c)2
- d)3
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A boat goes 8 km upstream and 12 km downstream in 7 hours. It goes 9 k...
Let speed of boat be x km/hr and speed of stream be y km/hr
Speed of boat upstream = x - y
Speed of boat downstream = x + y
According to question,
{8/(x - y)} + {12/(x + y)} = 7
⇒ 8x + 8y + 12x - 12y = 7(x2 - y2)
⇒ 20x - 4y = 7(x2 - y2) ----(1)
Also,
{9/(x - y)} + {18/(x + y)} = 9
⇒ x + y + 2x - 2y = (x2 - y2)
⇒ 3x - y = (x2 - y2)
⇒ 21x - 7y = 7(x2 - y2) ----(2)
Subtracting equation (1) from (2) we get,
⇒ x - 3y = 0
⇒ x = 3y
Now, from equation (1) we get,
⇒ 60y - 4y = 7(9y2 - y2)
⇒ 56y = 56y2
⇒ y(y - 1) = 0
⇒ y = 1
Now,
⇒ x = 3y = 3 × 1 = 3 km/hr
∴ the speed of the boat in still water = 3 km/hr
Most Upvoted Answer
A boat goes 8 km upstream and 12 km downstream in 7 hours. It goes 9 k...
Let's assume the speed of the boat in still water is 'x' km/h and the speed of the stream is 'y' km/h.
Upstream:
When the boat is moving upstream, its effective speed is reduced by the speed of the stream. So, the speed of the boat relative to the stream is (x - y) km/h.
Downstream:
When the boat is moving downstream, its effective speed is increased by the speed of the stream. So, the speed of the boat relative to the stream is (x + y) km/h.
From the given information, we can form two equations:
Equation 1:
8/(x - y) + 12/(x + y) = 7
Equation 2:
9/(x - y) + 18/(x + y) = 9
Now, let's solve these equations to find the values of x and y.
Solving Equation 1:
Multiplying both sides of the equation by (x - y)(x + y), we get:
8(x + y) + 12(x - y) = 7(x - y)(x + y)
8x + 8y + 12x - 12y = 7(x^2 - y^2)
20x - 4y = 7x^2 - 7y^2
Simplifying further:
7y^2 - 20x + 4y + 7x^2 = 0
Solving Equation 2:
Multiplying both sides of the equation by (x - y)(x + y), we get:
9(x + y) + 18(x - y) = 9(x - y)(x + y)
9x + 9y + 18x - 18y = 9(x^2 - y^2)
27x - 9y = 9x^2 - 9y^2
Simplifying further:
9y^2 - 27x + 9y + 9x^2 = 0
Now, we have two quadratic equations. Let's solve them simultaneously.
By equating the coefficients of x and y, we get:
20 = 7x
27 = 9x
Simplifying further, we find:
x = 3
Now, substituting the value of x into either equation, we can find the value of y:
27 = 9(3)
y = 0
Therefore, the speed of the boat in still water is 3 km/h (option D).
Upstream:
When the boat is moving upstream, its effective speed is reduced by the speed of the stream. So, the speed of the boat relative to the stream is (x - y) km/h.
Downstream:
When the boat is moving downstream, its effective speed is increased by the speed of the stream. So, the speed of the boat relative to the stream is (x + y) km/h.
From the given information, we can form two equations:
Equation 1:
8/(x - y) + 12/(x + y) = 7
Equation 2:
9/(x - y) + 18/(x + y) = 9
Now, let's solve these equations to find the values of x and y.
Solving Equation 1:
Multiplying both sides of the equation by (x - y)(x + y), we get:
8(x + y) + 12(x - y) = 7(x - y)(x + y)
8x + 8y + 12x - 12y = 7(x^2 - y^2)
20x - 4y = 7x^2 - 7y^2
Simplifying further:
7y^2 - 20x + 4y + 7x^2 = 0
Solving Equation 2:
Multiplying both sides of the equation by (x - y)(x + y), we get:
9(x + y) + 18(x - y) = 9(x - y)(x + y)
9x + 9y + 18x - 18y = 9(x^2 - y^2)
27x - 9y = 9x^2 - 9y^2
Simplifying further:
9y^2 - 27x + 9y + 9x^2 = 0
Now, we have two quadratic equations. Let's solve them simultaneously.
By equating the coefficients of x and y, we get:
20 = 7x
27 = 9x
Simplifying further, we find:
x = 3
Now, substituting the value of x into either equation, we can find the value of y:
27 = 9(3)
y = 0
Therefore, the speed of the boat in still water is 3 km/h (option D).
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A boat goes 8 km upstream and 12 km downstream in 7 hours. It goes 9 km upstream and 18 km downstream in 9 hours. What is the speed (in km/h) of the boat in still water?a)5b)4c)2d)3Correct answer is option 'D'. Can you explain this answer?
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A boat goes 8 km upstream and 12 km downstream in 7 hours. It goes 9 km upstream and 18 km downstream in 9 hours. What is the speed (in km/h) of the boat in still water?a)5b)4c)2d)3Correct answer is option 'D'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A boat goes 8 km upstream and 12 km downstream in 7 hours. It goes 9 km upstream and 18 km downstream in 9 hours. What is the speed (in km/h) of the boat in still water?a)5b)4c)2d)3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boat goes 8 km upstream and 12 km downstream in 7 hours. It goes 9 km upstream and 18 km downstream in 9 hours. What is the speed (in km/h) of the boat in still water?a)5b)4c)2d)3Correct answer is option 'D'. Can you explain this answer?.
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