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# BOATS

## BOATS SET4

1. Man can row 30km upstream & 44km downstream in 10 hrs. Also he run 40km upstream & 55km downstream in 13 hrs. Find the rate of the current & the speed of the man in still water ?A) 3 & 8 km/hrB) 2 & 5 km/hrC) 1 & 3 km/hrD) None of the aboveAns. AUpstream Downstream time30 44 1040 55 13Upstream = 30*55 – 40*44 / 44*13 – 55*10 = 5Downstream = 30*55 – 40*44 / 30*13 – 40*10 = 11Therefore, Rate of current = 11-5/2 = 3 km/hrSpeed of the man = 11+5/2 = 8 km/hr 2. A motor boat takes 2 hrs to travel a distance of a 9km down the current & it takes 6 hrs. to travel the same distance against the current. The speed of the boat(in km/hr) in still water & that of the current are A) 3,2B) 3,1C) 3.5,2.5D) 3,1.5Ans. DLet speed of boat in still water be x km/hr & speed of current be y km/hr9/x+y = 2& 9/ x-y =6X+y=9/2x-y = 9/6 = 3/2therefore, x=3 & y=1/2 km/hr 3. A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 84 km downstream.A) 4 hoursB) 5 hoursC) 6 hoursD) 7 hoursAns. ASpeed downstream = (16 + 5) = 21 kmph Time = distance/speed = 84/21 = 4 hours 4. A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back. how far is that place.A) 0.4 kmB) 1.4 kmC) 2.4 kmD) 3.4 kmAns. CLet the distance is x kmRate downstream = 5 + 1 = 6 kmphRate upstream = 5 – 1 = 4 kmphthen x/6 + x/4 = 1 [because distance/speed = time]=> 2x + 3x = 12 => x = 12/5 = 2.4 km 5. The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes isA) 1.6 kmB) 2 kmC) 3.6 kmD) 4 kmAns. CSpeed downstreams =(15 + 3)kmph= 18 kmph.Distance travelled = (18 x 12/60)km= 3.6km       iibm

## BOATS SET3

1. A man can row 913 kmph in still water and finds that it takes him thrice as much time to row up than as to row, down the same distance in the river. The speed of the current is.A) 323kmphB) 423kmphC) 523kmphD) 623kmphAns. BSpeed of current = 1/2(a-b) Let the speed upstream = x kmphThen speed downstream is = 3x kmph speed in still water = 12(a+b)=>12(3x+x)=>2x as per question we know, 2x=913=>2x=283=>x=143 So, Speed upstream = 14/3 km/hr, Speed downstream 14 km/hr. Speed of the current=12[14-143]=143=423kmph 2. A man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes. His rowing speed in still water isA) 4 kmphB) 5 kmphC) 6 kmphD) 7 kmphAns. BRate upstream = (750/675) = 10/9 m/sec Rate downstream (750/450) m/sec = 5/3 m/secRate in still water = (1/2)*[(10/9) + (5/3)] m/sec.= 25/18 m/sec = (25/18)*(18/5) kmph = 5 kmph 3. If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph, then the speed of the boat in still water isA) 12 kmphB) 13 kmphC) 14 kmphD) 15 kmphAns. BRate upstream = (7/42)*60 kmh = 10 kmph. Speed of stream = 3 kmph. Let speed in sttil water is x km/hr Then, speed upstream = (x ?3) km/hr. x-3 = 10 or x = 13 kmph 4. 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 stream isA) 3:1B) 1:3C) 2:4D) 4:2Ans. ALet speed downstream = x kmphThen Speed upstream = 2x kmph So ratio will be,(2x+x)/2 : (2x-x)/2 => 3x/2 : x/2 => 3:1 5. A man’s speed with the current is 20 kmph and speed of the current is 3 kmph. The Man’s speed against the current will beA) 11 kmphB) 12 kmphC) 14 kmphD) 17 kmphAns. CSpeed with current is 20,speed of the man + It is speed of the current Speed in still water = 20 – 3 = 17 Now speed against the current will be speed of the man – speed of the current= 17 – 3 = 14 kmph

## BOATS SET2

1. A man can row upstream 10 kmph and downstream 20 kmph. Find the man rate in still water and rate of the stream.A) 0,5B) 5,5C) 15,5D) 10,5Ans. CIf a is rate downstream and b is rate upstream Rate in still water = 1/2(a+b)Rate of current = 1/2(a-b) => Rate in still water = 1/2(20+10) = 15 kmph= Rate of current = 1/2(20-10) = 5 kmph 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 current.A) 1 km/hrB) 2 km/hrC) 3 km/hrD) 4 km/hrAns. AFirst of all, we know that speed of current = 1/2(speed downstream – speed upstream) [important] So we need to calculate speed downstream and speed upstream first. Speed = Distance / Time [important] Speed upstream =(15334)km/hr=15×415=4km/hrSpeed Downstream = (5212)km/hr=5×25=2km/hrSo speed of current = 12(4-2)=1km/hr 3. In one hour, a boat goes 11km along the stream and 5 km against it. Find the speed of the boat in still waterA) 6B) 7C) 8D) 9Ans. CWe know we can calculate it by 1/2(a+b) = 1/2(11+5) = 1/2(16) = 8 km/hr 4. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) isA) 2 km/hrB) 3 km/hrC) 4 km/hrD) 5 km/hrAns. DLet the speed of the stream be x km/hr. Then,Speed downstream = (15 + x) km/hr,Speed upstream = (15 – x) km/hr So we know from question that it took 4(1/2)hrs to travel back to same point. So, 3015+x-3015-x=412=>900225-x2=92=>9×2=225=>x=5km/hr 5. If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the stream isA) 5 km/hrB) 4 km/hrC) 2 km/hrD) 1 km/hrAns. DRate upstream = (15/3) kmph Rate downstream (21/3) kmph = 7 kmph. Speed of stream (1/2)(7 – 5)kmph = 1 kmph

## BOATS SET1

Q.1 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) & stream ?A) 3:1B) 2:1C) 4:1D) 5:1Ans. ALet upstream =2x km/hrDownstream = x km/hrBoat:Stream = (u+v/2) : (u-v/2)(2x+x / 2) : (2x-x / 2) Q.2 Boat covers a certain distance downstream in 1 hr, while it comes back in 1 ½ hrs. If the speed of the stream be 3 km/hr. What is the speed of the boat in still water ?A) 15 km/hrB) 16 km/hrC) 17 km/hrD) 18 km/hrAns. AShortcut:Speed= Z(x+y) / y-xOr 3 (1+ 3/2) / (3/2 – 1)= 15 km/hr Q.3 A man can row 15km/hr in still water. If he takes twice as long to row up as to row down the river. Find the rate of the stream ?A) 5 km/hrB) 6 km/hrC) 7 km/hrD) 8 km/hrAns. AShortcut:15+x = 2 (15 – x)15+x = 30-2xThus, x=5km/hr Q.4 Man can row 8km/hr in still water & the river is running at 2km/hr. If the man takes 1hr to row to a place & back. How far is the place ?A) 3.75 kmB) 4.75 kmC) 3.0 kmD) 4.0 kmAns. A Q.5 Man can row upstream at 10 km/hr & downstream at 16 km/hr. Find the man’s rate in still water & the rate of current ?A) 13 & 3 km/hrB) 12 & 2 km/hrC) 11 & 1 km/hrD) 13 & 2 km/hrAns. ARate in still water = ½ (10+16) = 26/2 = 13 km/hrRate of current = ½ (10-16) = 3 km/hr