[aptitude] boats and streams made-easy using our std-table method « mrunal

12/13/13 [Aptitude] Boats and Streams made-easy using our STD-Table Method Mrunal

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

Case#1: Basics

Case 2: Time same but Different distance covered in each case

Case #3: unknown variables

Previous Articles

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

DownstreamBoat 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 will increase and we can do addition.

Hence Downstream speed = speed of Boat PLUS speed of stream (B+S)

Upstream

Boat is moving against the direction of river. It is same like Pipe A can fill the tank in 2 hours while Pipe B can empty the tank in 1

hours

In short they work against each other, hence final speed is decreases so weve to subtract. (B-S)

Upstream speed = Speed of Boat MINUS speed of stre am (B-S)

Case#1: Basics

Question: A man can row Upstream @15kmph and downstream @21 kmph, what is the speedof 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

Time

Distance

As weve seen in earlier Time and work problems, we can do addition and subtraction in 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) from eq(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 it by 2 you get speed of column 2.then subtract column 2 from column 3 you get speed of column 1:See this Image

HOME APTITUDE APRIL 22ND, 2012 11 COMMENTS



DONE! No lengthy calculation required. But mind it: In the STD table, We can do direct addition, subtraction only for the speedcells 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 with next question

Case 2: Time same but Different distance covered in each case

Q. A Man rows the boat downstream for 60 km and Upstream 36 km, taking 4 hours eachtime. 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

Compare this with first case. We know the speeds of upstream and downstream, we can 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 correct.

Case #3: unknown variables

A boat sails downstream from point A to B, which is 10 km away from A, and then returns toA. If actual speed of the boat in still water is 3kmph, and the total upstream and downstreamjourney takes 12 hours. What must be the actual speed of boat for the trip from A to B to takeexactly 100 minutes.

Difficulty of a question doesnt depend on the length of question paragraph. Above sum has no dum in it, just like our PM. This canbe solved using the universal STD method.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 columns



Speed 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

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 in mind 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 :find Upstream 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 100 minutes.Rephrase:

We want to go downstream for 10 kilometers. Speed of river is 2 kmph. We want to cover thisdistance 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 A Special case: A to B

B alone S alone 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.



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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 by 60)

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 the boat at the speed of 4kmph.

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

vijayManikantaReply to this comment

Hi

In this article in case#3 I think question should be like following.

A boat sails downstream from point A to B, which is 10 km away from A, and then returns to A. If actual speed of the boat in still water is 3kmph, and total time

taken for the trip from A to B and B to A is 12 hours . What must be the actual speed of boat for the trip from A to B to take exactly 100 minutes.

B'coz for the question you have given the times will be 't' from A to B and 't+12" from B to A.

If I was wrong clarify

Mrunal Reply to this comment

yes question itself had mistake in wording.

but it is rectified now. Thanks for commenting.

amanzReply to this comment

really , well defined..

RajaniReply to this comment



Hi

Can anybody help me out by solving this problem in the method which Mrunal has said?

A man can row 40km upstream and 55km downstream in 13 hours also, he can row 30km upstream and 44km down stream in 10 hours. Find the speed of the

man in still water and the speed of the current.

plzzzzzzz help me out ASAP as i am preparing for NICL AO exam.


Can anybody plzzzzzzzzzzzz help me out with this question ASAP

shineReply to this comment

make the distance covered in upstream same . that is multiply the second case by 4/3 then the situation changes to 40 km in upstream and 44* 4/3 km in

downstream in 10* 4/3 hours. now compare with the first .take the differences. we get 176/3-55 km in downstream in 40/3 13 hours . That is 11/3 km in 1/3

hours. in 1 hour 11 kms downstream. So time taken to cover 55 km is 5 hours . The remaining 8 hours 40 km in upstream. So the speed in upstream is 5 km/hr.

So the speed of the current is (11-5)/2 =3 km/hr

speed of the man is 8 km /hr


Better be late than never.. any wayz if not helpful for the exam, atleast I got this problem solved and i got the method of solving it. Thank u so much

shineReply to this comment

Upstream downstream time

40 55 13

30 *4/3 44* 4/3 10*4/3 subtract first from the second

0 11/3 1/3

therefore speed in downstream is 11 km/hr. 55kms in 5hr and remaining 8 hour 40 km in upstream. Speed in up stream is 5km/hr

raj chauhanReply to this comment

graet job man !!

Shine RajReply to this comment

Thank You

MayankReply to this comment

when i clicked Case#1: Basics it says you have not permission even though i have made new a/c.

[aptitude] boats and streams made-easy using our std-table method « mrunal

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