Boats & Stream – Section1

 Question #1: A man can row downstream at the rate of 24 kmph and upstream at 7 kmph. Find the man’s rate in still water and rate of current. A) 14.6 kmph, 7.5 kmph B) 14.7 kmph, 7.8 kmph C) 15.6 kmph, 6.5 kmph D) 15.5 kmph, 8.5 kmph Option 'D' : 15.5 kmph, 8.5 kmph Hint: Rate of still water = 1/2 (down stream + upstream) = 1/2 (24 + 7) = 15.5 kmph rate of current = 1/2 (down stream - upstream) = 1/2 (24 - 7) = 1/2 (17) = 8.5 kmph Question #2: A man can row 24 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of the stream. A) 8 kmph B) 11 kmph C) 12 kmph D) 9 kmph Option 'C' : 12 kmph Hint: Let man's rate upsteam be X kmph Then his rate of downstream = 3X kmph Rate still water = 1/2 (3X + X) = 2X 2X = 24 X = 12 Rate of upstream = 12 Rate of downstream = 36 Rate of stream 1/2 ( 36 - 12) = 12 kmph Question #3: In a stream running at 2 kmph, a motor boat goes 10 km upstream and back again to the starting point in 55 minutes. Find the speed of motor boat in still water. A) 21 kmph B) 22 kmph C) 20 kmph D) 23 kmph Option 'B' : 22 kmph Hint: Let the speed of motor boat instill water be X kmph Then, speed in downstream = (X + 2) km and. speed in upstream = (X - 2) kmph Time taken to row 10km & back = (10/X+2,10/X-2) 10/X+2 + 10/X-2 = 55/60 11X2 - 240X - 44 = 0 (X - 22)(11x + 2) = 0 X = 22 or X = -2/11 Then X = 22 kmph Question #4: A man rows to a place 48 km distance and back in 14 hours. He finds that he can row 4 km with the stream in the same time 3 km against the stream. The rate off the stream is: A) 1 kmph B) 2 kmph C) 3 kmph D) 4 kmph Option 'A' : 1 kmph Hint: Let be moves 4km downstream in X Hours Then in speed downstream = kmph Speed in upstream = 4/X kmph 48/4/X + 48/3/X = 14 12X + 16X =14 X = 1/2 Speed in downstream = 8 kmph Speed in up stream = 6 kmph Then the Rate of stream = 1/2 (8 - 6) = 1 kmph Question #5: A man can row 8 kmph in still water. If the velocity of the current is 2 kmph and it takes him 2 hours to row to a place and come back, how far is the place? A) 3.4 km B) 7.5 km C) 5.5 km D) 5.7 km Option 'B' : 7.5 km Hint: Man's rate down stream = 8 + 2 = 10 kmph Man's rate upstream = 8 - 2 = 6 kmph Let the required distance be X km Then X/10 + X/6 = 2 3X + 5X = 60 8X = 60 X = 7.5 km Question #6: A boat can travel 8 km an hour in still water, but it takes thrice as much time for travelling the same distance against the current. The speed of the current (in kmph) is: A) 41 B) 47 C) 62 D) 51 Option 'A' : 41 Question #7: In an hour a boat goes 10 km along the stream and 4 km against the stream. The speed of the boat in still water (in kmph) is: A) 10 kmph B) 2 kmph C) 8 kmph D) 7 kmph Option 'D' : 7 kmph Hint: Let the speed of stream = X kmph and the speed of water = 8 kmph X + Y = 10 X - Y = 4 X = 7, Y = 3 Speed of stream = 7 kmph Question #8: A boat man goes 4 km against the current of the stream in 1 hour and goes 2 km along the current in 5 minutes. How long will it take to go 21 km in stationary water? A) 1 Hour B) 2 Hour 50 Minutes C) 1 Hour 15 Minutes D) 1 Hour 30 Minutes Option 'C' : 1 Hour 15 Minutes Question #9: A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively? A) 4 : 5 B) 7 : 4 C) 8 : 3 D) 5 : 7 Option 'C' : 8 : 3 Question #10: 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: A) 4 kmph B) 3 kmph C) 5 kmph D) 8 kmph Option 'D' : 8 kmph