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

In Aptitude by Support Staff

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

  1. Case: Train, Man and Bridge
    1. Conversion : kmph vs ms
    2. Finding length of train
  2. Case: Time n Work : A and B

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

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 equations
20s=M+180….(i)
8s=M….(ii)
So in first equation, replace the value of M=8s
20s=8s+180
20s-8s=180
12s=180
S=180/12
S=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 seconds
1km / 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 that
S x 8 =M
And we’ve found that speed of train= 15m/s.
hence 15 x 8 =m
m=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
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, meaning
So 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)a
Therefore, b=5a/3
Now 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 column
Speed x time = distance
8a/3 x T =80a
Therefore T= 30 days.
Final answer: if A and B work together, it’ll take them 30 days to finish the job.