[Aptitude Q] STD table : Application in train man bridge, time and work problems

1. Conversion : kmph vs ms2. Finding length of train

1. Case: Train, Man and Bridge

2. Case: Time n Work : A and B

Not really an article, just solving some readers’ queries to keep the STD concept refreshed.

Case: Train, Man and Bridge

A man is standing on a 180m long bridge.He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.Approach:

When train crosses the bridge When train crosses the man

Total distance= length of train + width of bridge length of train + width of bridge

“m”+180 “m”+0

Because in comparison to train, man / telephone wire / bike-rider etc are considered zero in width.Now make table

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Now make table

Train + bridge Train + man

Speed “s” “s”

Time 20 8

Distance M+180 M

Now apply STD formula and you get two equations

Train + bridge Train + man

Speed “s” “s”

Time 20 8

Distance M+180 M

Speed X time = Distance S x 20 = (M+180) S x 8 =M

Just solve those two equations20s=M+180….(i)8s=M….(ii)So in first equation, replace the value of M=8s20s=8s+18020s-8s=18012s=180S=180/12S=15 m/s. that’s our final answer. But suppose, in the answer options, the speed is given in in km/h, then you need to convert m/s into km/h.

Conversion : kmph vs ms

1km =1000 meters.1 hr = 60 minutes = 60 x 60 seconds = 3600 seconds.Therefore, 1 km / hr = 1000m / 3600 seconds1km / hr = 5 / 18 (m/s)In otherwords,1 meter per second = 18 / 5 kmph.So 15 (m/s) = 15 x (18/5) km/h = 54 kmph. That’s our final answer.

Finding length of train

Moving to the next part: find the length of this train.From the second equation, we know thatS x 8 =MAnd we’ve found that speed of train= 15m/s.hence 15 x 8 =mm=120meters.Answer: length of train is 120 meters.

Case: Time n Work : A and B

Question: A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how much time will A and B together finish the work?Make table

A B

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A B

Speed a b

Time 80 b

Distance = speed x time a x 10=80a

It means total distance to be covered, is “80a”.

A works for 10 days

A B A works

Speed a b a

Time 80 10

Distance = speed x time a x 10=80a 10 x a =10a

See the last column. A covered distance of 10a, meaningSo 80a-10a=70a distance is yet to be covered.Now B comes and finishes this in 42 days

A B A works B finishes

Speed a b a b

Time 80 10 42

Distance = speed x time

a x 10=80a

a x 10 =10a. (meaning 70a remains).

b x 42= 42b

That means 42b=70a (because remaining work =70a and B finished this.)b=(70/42)aTherefore, b=5a/3Now if A+B worked together then, we can add their speed. And together they’ve to finish 80a distance

Update the table

A B A works B finishes A+B together

Speed a b=5a/3 a b a+5a/3=8a/3

Time 80 10 42 T

Distance = speed x time

a x 10=80a

a x 10 =10a. (so 70a work remains).

b x 42= 42b

80a

Apply STD in last columnSpeed x time = distance8a/3 x T =80aTherefore T= 30 days.Final answer: if A and B work together, it’ll take them 30 days to finish the job.

Pasted from <http://mrunal.org/2013/02/aptitude-q-std-table-application-in-train-man-bridge-time-and-work-problems.html>

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