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A man can row against the current three-fourth of a kilometre in 15 minutes and returns the same distance in 10 minutes. The ratio of his speed to that of the current is
- a)3 : 5
- b)5 : 3
- c)1 : 5
- d)5 : 1
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A man can row against the current three-fourth of a kilometre in 15 m...
Speed of boat in still water = x kmph
Speed of current = y kmph
From equations (i) and (ii),
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A man can row against the current three-fourth of a kilometre in 15 m...
Let's assume the speed of the man in still water is x km/h and the speed of the current is y km/h.
Rowing against the current:
Distance = 3/4 km
Time = 15 minutes = 15/60 = 1/4 hour
Rowing with the current:
Distance = 3/4 km
Time = 10 minutes = 10/60 = 1/6 hour
To find the ratio of the man's speed to that of the current, we need to compare the time taken to cover the same distance in both cases.
Rowing against the current:
Speed of the man in still water = x km/h
Speed of the current = y km/h
Effective speed = (x - y) km/h
Distance = Speed * Time
3/4 = (x - y) * (1/4)
3 = x - y
Rowing with the current:
Speed of the man in still water = x km/h
Speed of the current = y km/h
Effective speed = (x + y) km/h
Distance = Speed * Time
3/4 = (x + y) * (1/6)
9/4 = x + y
Solving the two equations:
x - y = 3
x + y = 9/4
Adding the two equations:
2x = 15/4
x = 15/8
Substituting the value of x in the first equation:
15/8 - y = 3
y = 15/8 - 3
y = 15/8 - 24/8
y = -9/8
Since speed cannot be negative, we discard the negative value of y.
Therefore, the speed of the man in still water is 15/8 km/h and the speed of the current is 9/8 km/h.
The ratio of the man's speed to that of the current is:
(15/8) : (9/8)
= 15 : 9
= 5 : 3
Hence, the correct answer is option 'D' (5 : 1).
Rowing against the current:
Distance = 3/4 km
Time = 15 minutes = 15/60 = 1/4 hour
Rowing with the current:
Distance = 3/4 km
Time = 10 minutes = 10/60 = 1/6 hour
To find the ratio of the man's speed to that of the current, we need to compare the time taken to cover the same distance in both cases.
Rowing against the current:
Speed of the man in still water = x km/h
Speed of the current = y km/h
Effective speed = (x - y) km/h
Distance = Speed * Time
3/4 = (x - y) * (1/4)
3 = x - y
Rowing with the current:
Speed of the man in still water = x km/h
Speed of the current = y km/h
Effective speed = (x + y) km/h
Distance = Speed * Time
3/4 = (x + y) * (1/6)
9/4 = x + y
Solving the two equations:
x - y = 3
x + y = 9/4
Adding the two equations:
2x = 15/4
x = 15/8
Substituting the value of x in the first equation:
15/8 - y = 3
y = 15/8 - 3
y = 15/8 - 24/8
y = -9/8
Since speed cannot be negative, we discard the negative value of y.
Therefore, the speed of the man in still water is 15/8 km/h and the speed of the current is 9/8 km/h.
The ratio of the man's speed to that of the current is:
(15/8) : (9/8)
= 15 : 9
= 5 : 3
Hence, the correct answer is option 'D' (5 : 1).
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A man can row against the current three-fourth of a kilometre in 15 minutes and returns the same distance in 10 minutes. The ratio of his speed to that of the current isa)3 : 5b)5 : 3c)1 : 5d)5 : 1Correct answer is option 'D'. Can you explain this answer?
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