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[Aptitude] Boats and Streams made-easy using our STD-Table Method

Case#1: Basics1.Case 2: Time same but Different distance covered in each case2.Case #3: unknown variables3.Previous Articles4.

I hope youve mastered the STD table method from earlier articles on Time and Work /Pipes and Cistern.We can use that STD method even in boats and streams question as well.

But first some terminologies

Downstream

Boat is moving along with flow of river (B), so water stream (S)helps the boat to move faster.It is same like A and B work together. So their speed willincrease and we can do addition.Hence Downstream speed = speed of Boat PLUS speed ofstream (B+S)

Upstream

Boat is moving against the direction of river. It is same like PipeA can fill the tank in 2 hours while Pipe B can empty the tank in1 hoursIn short they work against each other, hence final speed isdecreases so weve to subtract. (B-S)Upstream speed = Speed of Boat MINUS speed of stream(B-S)

Case#1: BasicsQuestion: A man can row Upstream @15kmph and downstream @21 kmph, whatis the speed of water in river?Now construct the usual STD table from the given data

B alone S alone Downstream (B+S) Upstream (B-S)

Speed ?? 21 15

Mrunal [Aptitude] Boats and Streams made-easy using our STD-Table Me... http://mrunal.org/2012/04/aptitude-boats-and-streams-made-easy.html/print/

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Time

Distance

As weve seen in earlier Time and work problems, we can do addition and subtractionin the Speed cells directly.B+S=21..eq(1)B-S=15eq(2)Add both equations(B+S) PLUS (B-S) = 21 PLUS 152B=36B=36/2B=18 kmphWe already know thatB+S=21SO IF B is 18 kmph then S = 21 minus 18 = 3 kmph.Answer: Speed of water is 3 kmph.[Alternatively: You can directly calculate speed of water by subtracting eq(1) fromeq(2)]

Shortcut Method

Above equations only for showing you the concept.Otherwise in the exam hall you can directly subtract column 4 from column 3, divide itby 2 you get speed of column 2.then subtract column 2 from column 3 you get speed of column 1:See this Image


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DONE! No lengthy calculation required. But mind it: In the STD table, We can dodirect addition, subtraction only for the speed cells and not for time cells.You can also verify the answer from the table.


Speed 18 3 21 15

Time

Distance

From the first two columns B minus S= 18 minus 3 = 15.In the last column, you can see that Upstream (B-S) = 15.So yes answer is correct.Anyways this was quite easy no brainer. Time to make things a bit complicated withnext questionCase 2: Time same but Different distance covered in each caseQ. A Man rows the boat downstream for 60 km and Upstream 36 km, taking 4hours each time. What is the speed of this boat?Fill up the STD table


Speed ??

Time 4 4

Distance 60 36

Apply the STD formula on third columnSpeed x Time = DistanceSpeed x 4= 60Speed = 60/4Downstream speed =15 kmphSame way calculate for fourth column, youll get upstream speed = 36/4=9kmphUpdate the table


Speed ?? 15 9

Time 4 4

Distance 60 36

Shortcut method revisited


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Compare this with first case. We know the speeds of upstream and downstream, wecan use the shortcut method.

For those still uncomfortable with shortcut method, just do it manuallyB+S=15 ; from column 4B-S=9 from column 3add both equations(B+S) PLUS (B-S) = 15 PLUS 92B=24B==24/2 =12 kmphAnswer. Speed of boat is 12 km per hour.

Verify the answer

So far weve calculated thatB+S=15 andB=12.Hence S=15 minus B=15 minus 12 =3kmphUpdate the table


Speed 12 3 15 9

Time 4 4

Distance 60 36

For the speed cells, Column 1 minus column 2 equals column 4. Hence answer is


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correct.

Case #3: unknown variablesA boat sails downstream from point A to B, which is 10 km away from A, andthen returns to A. If actual speed of the boat in still water is 3kmph, and the totalupstream and downstream journey takes 12 hours. What must be the actualspeed of boat for the trip from A to B to take exactly 100 minutes.Difficulty of a question doesnt depend on the length of question paragraph. Above sumhas no dum in it, just like our PM. This can be solved using the universal STDmethod.Given in the problem:Speed of boat in still water (B alone) =3kmphLength of river =10kmWe know that total time taken for upstream+ downstream=12 hours.Suppose upstream takes journey takes t hours, then downstream journey takes=(12-t) hours. Fill up the table

From A to B From B to A


Speed 3 ?? 3+s 3-s

Time 12-t t

Distance 10 10

Apply the STD formula for both upstream and downstream columnsSpeed x time = distance(3+s)*(12-t)=10 (t-12)=10/(3+s)eq(1)(3-s)*(t)=10t=10/(3-s)eq(2)The total time taken in upstream + downstream journey(12-t)+ t=12Substitute the values of (12-t) and (t) with the things from eq 1 and 2

See this image for calculation


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Therefore

S2=9-5=4

MIND IT: Square Roots

S2=4 that doesnt mean s=2 only.Because square of (-2) =(-2)*(-2)=(+4)When you take square root of 4, it can be (+2) or (-2)But Since speed of water is a positive value, well use s=(+2). But keep this thing inmind especially for data-sufficiency problems.Update the table

From A to B From B to A


Speed 3 2 3+2=5 3-2=1

Time 12-t t

Distance 10 10

We are not concerned with finding time in this question but still for practice :findUpstream timeSpeed xtime = distance1 x t =10t = 10/1=10 hours.Upstream time is 10 hours.Similarly downstream time is 2 hours. (apply STD or use 12-t, answer is 2 hours)Coming to the ultimate questionWhat must be the actual speed of boat for the trip from A to B to take exactly 100minutes.


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Rephrase:We want to go downstream for 10 kilometers. Speed of river is 2 kmph. We wantto cover this distance in exactly 100 minutes, how fast should we run this boat?Make a new columnAssume that new speed of boat should be (Bn)

From A to B From B to ASpecial case: A toB

Balone

Salone

Downstream(B+S)

Upstream(B-S)

Downstream(Bn+S)

Speed 3 2 5 1 (Bn+2)

Time 2 hrs 10 hrs 100 minutes

Distance 10 10 10

MIND IT: all units must be in same format

To get correct answers in STD formula, everything must be in same format.Either kilometer-hour format OR metre-second formatLets stick to hours in this case.Convert 100 minutes into hours60 minutes =1 hour1 minute =1/60 hourMultiply both sides with 100100 minutes = (100/60) hours.(In short: When you want to convert minutes into hours, just divide minutes by60)Apply STD formula on last column

Speed x time = distance(Bn+2) x 100/60=10

(Bn+2) =6010/100

(Bn+2) =6

Bn=6-2

Bn=4 kmph

Final answer: if we wish to cover 10 km downstream in 100 minutes, we must run theboat at the speed of 4kmph.For previous Articles on Aptitude, visit Mrunal.org/aptitude

URL to article: http://mrunal.org/2012/04/aptitude-boats-and-streams-made-easy.html

Posted By Mrunal On 22/04/2012 @ 16:57 In the category Aptitude


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