Aptitude Boat And StreamPage 3

17.

A motorboat, whose speed is 15 kmph in still water goes 30 km downstream and come back in a total of 4 hours 30 minutes. The speed of the stream (in kmph) is:
(a)4 kmph
(b)5 kmph
(c)6 kmph
(d)10 kmph
Answer is: BLet the speed of the stream be X kmph. Then,
Speed downstream = (15 + X) kmph
Speed upstream = (15 – X) kmph
∴ 30/(15 + X) + 30/(15 – X) = 9/2
⇒ 900/(225 – X²) = 9/2
⇒ 9X² = 225
⇒ X² = 25
⇒X = 5 kmph

18.

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:
(a)2 mph
(b)2.5 mph
(c)3 mph
(d)4 mph
Answer is: ALet the speed of the stream be X mph. Then,
Speed downstream = (10 + X) mph, Speed upstream = (10 – X) mph.
∴ 36/(10 – X) – 36/(10 + X) = 90/60
⇒ 72X x 60 = 90 (100 - X²)
⇒ X² + 48X + 100 = 0
⇒ (X + 50) (X – 2) = 0
⇒ X = 2 mph

19.

A man rows to a place 48 km distantce and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
(a)1 kmph
(b)1.5 kmph
(c)1.8 kmph
(d)3.5 kmph
Answer is: ASuppose he moves 4 km downstream in X hr. Then,
Speed downstream = (4/X) kmpm.
Speed upstream = (3/X) kmph.
∴ 48/(4/X) + 48/(3/X) = 14
X = 1/2
So, Speed downstream = 8 kmph,
Speed upstream = 6 kmph
Rate of the stream = 1/2 x (8 - 6) kmph = 1 kmph

20.

A man can row 40 km upstream and 55 km downstream in 13 hours. Also, he can row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the man in still water and the speed of the current?
(a)8 kmph , 3 kmph
(b)5 kmph, 6 kmph
(c)7 kmph, 3 kmph
(d)6 kmph, 5 kmph
Answer is: ALet rate upstream = X kmph and rate downstream = Y kmph
Then, 40/X + 55/Y =13 ..….(i)
and 30/X + 44/Y = 10 …..(ii)
Multiplying (ii) by 4 and (i) by 3 and subtracting,
we get : 11/Y = 1 or Y = 11
Substituting Y = 11 in (i),
we get : X = 5
∴ Rate in still water = 1/2 x (11 + 5) kmph = 8kmph
Rate of current = 1/2 x (11 – 5) kmph = 3 kmph.

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