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A Boat going upstream takes 8 hours 24 minutes to cover a certain distance, while it takes 5 hours to cover 5/7 of the same distance running downstream.Then what is the ratio of the speed of boat to speed of water current?

  • a)
    6:5

  • b)
    11:5

  • c)
    11:6

  • d)
    11:1

  • e)
    11:10

Correct answer is option 'D'. Can you explain this answer?
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A Boat going upstream takes 8 hours 24 minutes to cover a certain dist...




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A Boat going upstream takes 8 hours 24 minutes to cover a certain dist...
Given information:
- Boat takes 8 hours 24 minutes to cover a certain distance upstream.
- Boat takes 5 hours to cover 5/7 of the same distance downstream.

To find: Ratio of speed of boat to speed of water current.

Let the speed of boat in still water be x and the speed of water current be y.

Calculations:
- Let's first calculate the speed of boat upstream.
- Distance covered upstream = speed * time
- Let the distance be d.
- d = (x - y) * (8 + 24/60) (Converting 8 hours 24 minutes into hours)
- d = (x - y) * (504/60)
- d = (x - y) * 8.4 (Multiplying and simplifying)
- Now let's calculate the speed of boat downstream.
- Distance covered downstream = speed * time
- Let the distance be 5/7 of d.
- 5/7 * d = (x + y) * 5
- 5/7 * d = (x + y) * 5
- d = (x + y) * 7 (Dividing both sides by 5/7)
- Now we have two equations with two variables. We can solve for x and y.
- d = 8.4(x - y) (Equation 1)
- d = 7(x + y) (Equation 2)
- From Equation 2, we get:
- x + y = d/7
- From Equation 1, we get:
- x - y = d/8.4
- Adding the above two equations, we get:
- 2x = d/7 + d/8.4
- 2x = (12.6d + 14d)/117.6
- 2x = 26.6d/117.6
- x = 13.3d/117.6
- Now substituting x in one of the equations, we can find y.
- x + y = d/7
- 13.3d/117.6 + y = d/7
- y = d/7 - 13.3d/117.6
- y = (16.8d - 13.3d)/117.6
- y = 3.5d/117.6

The required ratio is x:y = (13.3d/117.6):(3.5d/117.6) = 11:1

Therefore, the answer is option D.
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A Boat going upstream takes 8 hours 24 minutes to cover a certain distance, while it takes 5 hours to cover 5/7 of the same distance running downstream.Then what is the ratio of the speed of boat to speed of water current?a)6:5b)11:5c)11:6d)11:1e)11:10Correct answer is option 'D'. Can you explain this answer?
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