Quantitative Aptitude
BOATS AND STREAMS MCQs
Speed in still water = \(\frac{1}{2}\) (11 + 5) kmph = 8 kmph.
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.
Speed downstream = (15 + 3) kmph = 18 kmph.
.Distance travelled = \(\left(18\times\frac{12}{60}\right)km\) = 3.6 km
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.
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.
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.
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
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.
Speed upstream = 7.5 kmph.
Speed downstream = 10.5 kmph.
So, Total time taken = \(\left(\frac{105}{7.5}+\frac{105}{10.5}\right)hours =24hours\)
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