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Quantitative Aptitude

BOATS AND STREAMS MCQs

Total Questions : 948 | Page 3 of 95 pages
Question 21.

In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:

  1.    3 km/hr
  2.    5 km/hr
  3.    8 km/hr
  4.    9 km/hr
 Discuss Question
Answer: Option C. -> 8 km/hr

Speed in still water =  \(\frac{1}{2}\)  (11 + 5) kmph = 8 kmph.

Question 22.

A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?

  1.    4 km/hr
  2.    6 km/hr
  3.    8 km/hr
  4.    Data inadequate
 Discuss Question
Answer: Option B. -> 6 km/hr

Rate downstream =    \(\left(\frac{16}{2}\right)kmph\)  = 8 kmph


Rate upstream =    \(\left(\frac{16}{4}\right)kmph\) = 4 kmph


Speed in still water =  \(\frac{1}{2}\)  (8 + 4) kmph = 6 kmph.

Question 23.

The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:

  1.    1.2 km
  2.    1.8 km
  3.    2.4 km
  4.    3.6 km
 Discuss Question
Answer: Option D. -> 3.6 km

Speed downstream = (15 + 3) kmph = 18 kmph.


.Distance travelled =    \(\left(18\times\frac{12}{60}\right)km\)  = 3.6 km

Question 24.

A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:

  1.    2 mph
  2.    2.5 mph
  3.    3 mph
  4.    4 mph
 Discuss Question
Answer: Option A. -> 2 mph

Let the speed of the stream x mph. Then,


Speed downstream = (10 + x) mph,


Speed upstream = (10 - x) mph.


So, \(\frac{36}{(10-x)}-\frac{36}{(10+x)}=\frac{90}{60}\)


 72x x 60 = 90 (100 - x2)


 x2 + 48x - 100 = 0


 (x+ 50)(x - 2) = 0


 x = 2 mph.

Question 25.

A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?

  1.    2.4 km
  2.    2.5 km
  3.    3 km
  4.    3.6 km
 Discuss Question
Answer: Option A. -> 2.4 km

Speed downstream = (5 + 1) kmph = 6 kmph.


Speed upstream = (5 - 1) kmph = 4 kmph.


Let the required distance be x km.


Then, \(\frac{x}{6}+\frac{x}{4} = 1 \)


 2x + 3x = 12


 5x = 12


 x = 2.4 km.

Question 26.

A boat covers a certain distance downstream in 1 hour, while it comes back in 1 \(\frac{1}{2}\) hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?

  1.    12 kmph
  2.    13 kmph
  3.    14 kmph
  4.    15 kmph
 Discuss Question
Answer: Option D. -> 15 kmph

Let the speed of the boat in still water be x kmph. Then,


Speed downstream = (x + 3) kmph,


Speed upstream = (x - 3) kmph.


So,  (x + 3) x 1 = (x - 3) x \(\frac{3}{2}
\)


 2x + 6 = 3x - 9


 x = 15 kmph.

Question 27.

A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?

  1.    40 minutes
  2.    1 hour
  3.    1 hr 15 min
  4.    1 hr 30 min
 Discuss Question
Answer: Option C. -> 1 hr 15 min

Rate downstream =     \(\left(\frac{1}{10}\times60\right)\)  km/hr = 6 km/hr


Rate upstream = 2 km/hr.


Speed in still water =    \(\frac{1}{2}\)  (6 + 2) km/hr = 4 km/hr.


So, Required time =   \(\left(\frac{4}{5}\right)\) hrs   =   \(1\frac{1}{4} hrs\)   = 1hr15min

Question 28.

A man can row three-quarters of a kilometre against the stream in 11 \(\frac{1}{4}\) minutes and down the stream in 7 \(\frac{1}{2}\) minutes. The speed (in km/hr) of the man in still water is:

  1.    2
  2.    3
  3.    4
  4.    5
 Discuss Question
Answer: Option D. -> 5

We can write three-quarters of a kilometre as 750 metres,


and 11 \(\frac{1}{4}\) minutes as 675 seconds.


Rate upstream = \(\left(\frac{750}{675}\right)m/sec = \frac{10}{9}m/sec.\)


Rate downstream = \(\left(\frac{750}{450}\right)m/sec = \frac{3}{5}m/sec.\)


So, Rate in still water = \(\frac{1}{2}\left(\frac{10}{9}+\frac{3}{5}\right)m/sec\)


= \(\frac{25}{18}m/sec.\)


\(\left(\frac{25}{18}\times\frac{18}{5}\right)km/hr\)


= 5 km/hr.

Question 29.

Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:

  1.    16 hours
  2.    18 hours
  3.    20 hours
  4.    24 hours
 Discuss Question
Answer: Option D. -> 24 hours

Speed upstream = 7.5 kmph.


Speed downstream = 10.5 kmph.


So, Total time taken = \(\left(\frac{105}{7.5}+\frac{105}{10.5}\right)hours =24hours\)

Question 30.

A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:

  1.    2 : 1
  2.    3 : 1
  3.    3 : 2
  4.    4 : 3
 Discuss Question
Answer: Option B. -> 3 : 1

Let man's rate upstream be x kmph.


Then, his rate downstream = 2x kmph.


So, (Speed in still water) : (Speed of stream) = \(\left(\frac{2x+x}{2}\right):\left(\frac{2x-x}{2}\right)\)


= \(\frac{3x}{2}:\frac{x}{2}\)


=3:1

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