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Boats and Streams

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Question
SSCCGLENQA12042982
Wired Faculty App

A boat covers 12 km upstream and 18 km downstream in 3 hours, while it covers 36 km upstream and 24 km downstream in 6 1 half space hours. What is the speed of the current?

  • 1.5 km/hr

  • 1 km/hr

  • 2 km/hr

  • 2.5 km/hr

Solution

C.

2 km/hr

If the speed of boat in still water be x kmph and that of current by y kmph, then
fraction numerator 12 over denominator straight x minus straight y end fraction space plus space fraction numerator 18 over denominator straight x space plus space straight y end fraction space equals space 3        ...(i)
fraction numerator 36 over denominator straight x minus straight y end fraction space plus space fraction numerator 24 over denominator straight x plus straight y end fraction space equals space 13 over 2 space space space space space space space... left parenthesis ii right parenthesis
By equation (i) x 3 - equation (ii)
rightwards double arrow space space space space fraction numerator 54 over denominator straight x plus straight y end fraction space minus space fraction numerator 24 over denominator straight x plus straight y end fraction space equals space 9 minus 13 over 2 rightwards double arrow space space fraction numerator 30 over denominator straight x plus straight y end fraction space space equals space 5 over 2 space rightwards double arrow space space straight x space plus space straight y space equals space 12 space space space space space... left parenthesis iii right parenthesis
From equation (i),
rightwards double arrow space space space space fraction numerator 12 over denominator straight x minus straight y end fraction space plus space 18 over 12 space equals space 3 rightwards double arrow space space space space fraction numerator 12 over denominator straight x minus straight y end fraction space equals space 3 minus 3 over 2 space equals space 3 over 2 rightwards double arrow space space space space straight x minus straight y space equals space fraction numerator 12 space cross times space 2 over denominator 3 end fraction space equals space 8 space space space space space space space space... left parenthesis iv right parenthesis
∴  Speed of current equals space 1 half left parenthesis 12 minus 8 right parenthesis space equals space 2 space kmph

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Question
SSCCGLENQA12043161
Wired Faculty App

A boat moves downstream at the rate of 1 km in 7 1 half space minutes and upstream at the rate of 5 km an hour. what is the speed of the boat in the still water?

  • 3 1 half space km divided by hour
  • 6 1 half space km divided by hour

  • 4 km/hour

  • 8 km/hour

Solution

B.

6 1 half space km divided by hour

Rate downstream of boat
 equals space open parentheses fraction numerator 1 over denominator begin display style fraction numerator 15 over denominator 2 space cross times space 60 end fraction end style end fraction close parentheses space kmph equals space fraction numerator 2 space cross times space 60 over denominator 15 end fraction space equals space 8 space kmph
Rate downstream of boat = 5 kmph
Speed of boat in still water = 1 half left parenthesis Rate space downstream space plus space Rate space upstream right parenthesis
      equals space 1 half left parenthesis 8 plus 5 right parenthesis space equals space 13 over 2 space equals space 6 1 half space kmph

Question
SSCCGLENQA12042125
Wired Faculty App

A man can row 15 km per hour downstream and 9 km per hour upstream. The speed (in kmph) of the boat in still water is

  • 10

  • 12

  • 15

  • 8

Solution

B.

12

Speed of boat in still water
    equals space 1 half left parenthesis Rate space Downstream space space plus space Rate space Upstream right parenthesis
   equals space 1 half open parentheses 15 space plus space 9 close parentheses kmph equals space 12 space kmph

Question
SSCCGLENQA12043128
Wired Faculty App

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

  • 3 : 5

  • 5 : 3

  • 1 : 5

  • 5 : 1

Solution

D.

5 : 1

Speed of boat in still water = x kmph
Speed of current  = y kmph
therefore space space space space straight x space minus space straight y space equals space fraction numerator begin display style 3 over 4 end style over denominator begin display style 15 over 60 end style end fraction space equals space 3 space space space space space... left parenthesis straight i right parenthesis
straight x space plus space straight y space equals space fraction numerator begin display style 3 over 4 end style over denominator begin display style 10 over 60 end style end fraction space space equals space 3 over 4 space cross times space 6 space equals space 9 over 2 space space space... left parenthesis ii right parenthesis
From equations (i) and (ii),
  2 straight x space equals space 3 plus space 9 over 2 space equals space 15 over 2 therefore space space space straight x space equals space 15 over 4 kmph
From equation (ii)
straight y space equals space 9 over 2 minus 15 over 4 space equals space fraction numerator 18 minus 15 over denominator 4 end fraction space equals 3 over 4 space kmph
therefore space space space straight x space colon space straight y space equals space 15 over 4 space colon space 3 over 4 space equals space 5 space colon space 1

Question
SSCCGLENQA12043467
Wired Faculty App

If the speed of a boat in still water is 20 km/hr and the speed of the current is 5 km/hr, then the time taken by the boat to travel 100 km with the current is

  • 2 hours

  • 3 hours

  • 4 hours

  • 7 hours

Solution

C.

4 hours

Distance  = 100 km

Speed of boat in still water = 20 km/hr

Speed of current  = 5 km/hr

Relative speed = (20 + 5)km/hr = 25 km/hr

Required Time

equals space open parentheses 100 over 25 close parentheses space equals space 4 space km divided by hr

 

 

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