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The time taken to cover an upstream distance from a point A to B is 3 hours more than the time taken to cover downstream distance from B to A. If the downstream speed of boat be 15 km/hr and the ratio between speed of boat in still water and speed of stream be 4:1 then what will be the distance from A to B? 
  • a)
    75 km
  • b)
    67.5 km
  • c)
    82 km
  • d)
    61 km
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?
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The time taken to cover an upstream distance from a point A to B is 3 ...
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The time taken to cover an upstream distance from a point A to B is 3 ...
Given Data:
Speed of boat in still water : Speed of stream = 4:1
Downstream speed = 15 km/hr

Let's assume:
Speed of boat in still water = 4x
Speed of stream = x

Calculating:
Speed downstream = 4x + x = 5x
Speed downstream = 15 km/hr
5x = 15
x = 3
Speed of boat in still water = 4*3 = 12 km/hr
Speed of stream = 3 km/hr

Time calculations:
Let the distance between A and B be D km
Time taken to cover downstream distance = D / (12+3) = D / 15
Time taken to cover upstream distance = D / (12-3) = D / 9
Given that time taken upstream is 3 hours more than time taken downstream:
D / 9 = D / 15 + 3
Multiplying by 45 to eliminate denominators: 5D = 3D + 45
2D = 45
D = 22.5 km
Therefore, the distance from A to B is 22.5 * 3 = 67.5 km, which corresponds to option (b).
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The time taken to cover an upstream distance from a point A to B is 3 hours more than the time taken to cover downstream distance from B to A. If the downstream speed of boat be 15 km/hr and the ratio between speed of boat in still water and speed of stream be 4:1 then what will be the distance from A to B?a)75 kmb)67.5 kmc)82 kmd)61 kme)None of theseCorrect answer is option 'B'. Can you explain this answer?
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