


1.
A man can row upstream at 7 kmph and downstream at 10 kmph. Find man's rate in still water and the rate of current.
2.
A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the river current in km/hr.
3.
A man can row 18 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of stream.
4.
There is a road beside a river. Two friends started from a place A, moved to a temple situated at another place B and then returned to A again. One of them moves on a cycle at a speed of 12 km/hr, while the other sails on a boat at a speed of 10 km/hr. If the river flows at the speed of 4 km/hr, which of the two friends will return to place A first? [R.R.B. 2001]
Answer & Solution
Answer: (B) Cycle
Solution: Clearly, the cyclist moves both ways at a speed of 12 km/hr. So, average speed of the cyclist = 12 km/hr. The boat sailor moves downstream @ (10 + 4) i.e., 14 km/hr and upstream @ (10  4) i.e, 6 km/hr. So, average speed of th boat sailor = [(2 * 14 * 6) / (14 + 6)] km/hr = 42/5 km/hr = 8.4 km/hr. Sine, the average speed of the cyclist is greater, he will return to A first. 5.
A man can row 7 1/2 kmph in still water. If in a river running at 1.5 km an hour, it takes him 50 minutes to row to a place and back, how far off is the place? [R.R.B. 2002]
6.
In a stream running at 2 kmph, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water.
Answer & Solution
Answer: (D)) 22 kmph
Solution: Let the speed of the motorboat in still water be x kmph. Then, Speed downstream = (x + 2) kmph; Speed upstream = (x  2) kmph. [6 / (x +2)] + [6 / (x  2)] = 33/60 => 11 (x^2)  240 x  44 = 0 => 11 (x^2)  242 x + 2x  44 = 0 => (x  22) (11x + 2) = 0 => x = 22 Hence, speed of motorboat in still water = 22 kmph. 7.
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.
Answer & Solution
Answer: (D) 8 kmph, 3 kmph
Solution: Let rate upstream = x km/hr and rate downstream = y km/hr. Then, (40/x) + (55/y) = 13 .... (i) (30/x) + (44/y) = 10 ..... (ii) Multiplying (ii) by 4 and (i) by 3 and subtracting, we get: 11/y = 1 => y = 11. Subtracting y = 11 in (i), we get : x = 5. Rate in still water = 1/2 [11 + 5] kmph = 8 kmph. Rate of current = 1/2 [11  5] kmph = 3 kmph. 