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
| 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.
![[Reasoning] Calendar Questions: Finding day or date, concepts, shortcuts explained](https://mrunal.org/wp-content/uploads/2013/01/i-lr-500x383.png)
Hi mrunal, should it not be 54 km/hr in first question??
CONVERTION KMPH VS MS:- Mrunal when u converted the speed of the train from m/s to km/hr u committed a mistake. the answer should be 54km/hr :- 15m/s= 15×18/5km/hr =54km/hr
corrected. thanks
sir, i find many of your articles worth saving!how can i download them????
Sir
Thanks for all the guidance and support you are providing to us. My maths is improving day by day and i am able to solve sums faster than what i used to do before.
I am going to take the SSC exam this year. If you can upload the SSC’s last 5-10 years paper, it will be beneficial to us.
Thanks
chandu for every article posted in mrunal . there is a link on right side bottom corner of every which can be used to save the article as a PDF file.
sir , in your approach ‘when train crosses the man’ shouldn’t it come ‘length of train+ width of man’ ?
Hi Mrunal , will u plzz tell how to prepare for general awareness section of sbi po .
with regards,
Shivesh
thnks
plz keep going on wid aptitude nd maths.
The best things in life is always FREE …/
good work mrunal…keep going.
will alwys need ur help…thankyou from everyone.
good work mrunal…keep going.thankyou from everyone.
sir there are no options to download this chapter. it would be great if you give the option for downloading it in pdf file.
After every article right corner there is a option called PDF/PRINT, go to that and you find options on ur left side and give the command to save as pdf you file will be saved in pdf.
My math is very poor I need your help sir Please!
Sir, Thank you for your guidance. I have a doubt in the following problem.
A train running at 54kmph takes 20sec to pass a platform. Next it takes 12 sec to pass a man walking at 6kmph in the same direction in which the train is going. Find the length of the train and length of the platform.
First the relative speed is calculated since the train and man in the same direction. (54-6 = 48). conversion = 40/3m/sec.
After that, I have doubt to proceed. Please guide me to proceed further in this problem.
as in 1st qus …
whn train moves with 54km/h
1-length of train will be-108m
2-length of platform will be-192m
and next 1is…
the speed of goods train will be 62 km/h
it is not so difficult to solve train jst do more practice and don’t go with formulas…basic method is always cool…..
Sir, I have one doubt in the following problem.
A man sitting in a train which is travelling at 50kmph observes that a goods train, travelling in opposite direction, takes 9 sec to pass him. If the goods train is 280m long, find its speed.
I am confused here in calculating the relative speed and how to observe the time taken to pass him. Please guide me to proceed.
Sir, I have one doubt in the following problem.
A man sitting in a train which is travelling at 50kmph observes that a goods train, travelling in opposite direction, takes 9 sec to pass him. If the goods train is 280m long, find its speed.
I am confused here in calculating the relative speed and how to observe the time taken to pass him. Please guide me to proceed
in this we consider only length of of goods train .so total length /a+b =time length=280m,a=50kmph=125/9metre per second ,let speed of second train is b metre per second so 280/125/9+b =9,b=280/9-125/9 =155/9=62 kmph
kindly provide practice problems
can’t we do m/8=(m+180)/20 to find the length of the train as speed in both the cases is same
Whether this problem is right?
A man walking in fog @ 4kmph. A 20m long train overtakes him in 30 seconds and the man could see in the fog uptoa distance of 50m. Find the speed of the train.
If right then please answer.
as in 1st qus …
whn train moves with 54km/h
1-length of train will be-108m
2-length of platform will be-192m
and next 1is…
the speed of goods train will be 62 km/h
it is not so difficult to solve train jst do more practice and don’t go with formulas…basic method is always cool…..
how can i solve this question with help of STD method:-
3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
3*8*2=x*4*1 x=48/4=12hours per day
Sir, kindly provide the solution for 2013 Pre STD problems by STD table & Product consistency method. I’m unable to arrive at solution by either method. May be m putting values wrong. & sir also kindly provide more Mock problems on STD specifically for solving. Thanks.
thank you mrunal for the time consuming method… keep guiding us
Two typists of varying skills can do a typing job in 6 min , if they work together.If the first typist typed alone for 4 min and then the second typiest typed alone for 6 min , they would be left with 1/5 of the whole work.How many minutes would it take the slower typiest to complete the typing job working alone?
Solve.. if u r mathematics Genius…??kese solve hoga by std rule
Hi sir, I find your tricks and methods very effective. Majority of questions I can solve with std table but I m stuck with this question. The answer displayed is 10 but my answer is 30. Please tell me how to solve this
Q). 10 men can complete a work in 6 days. 12 women can complete in 10 days and 10 children in 12 days. 1 man, 1 woman and 1 child started the work. In how many days will the work get completed if the man did twice the work as woman and also twice the work as child?