Aptitude - Problems on Trains - Discussion

Why we are multiplying the 60 with 5/18?

The answer is simple. We are converting the 'kilo-meters/hour' value into 'meters/second'.

Let me explain about converting km/hr into m/s in detail.

1 km = 1000 meters.
1 hr = 3600 seconds.

1 km/hr = 1000/3600 m/s

= 10/36 m/s

= 5/18 m/s.

Therefore 1 km/hr = 5/18 m/sec.

Similarly 60 km/hr = 60 x 5/18 m/sec.

You may ask me, why should I convert it from km/hr to m/sec?

Because, the time taken by the train is given in terms of seconds (9 seconds) and the 4 options are in terms of metres. But the speed of the train is given in terms of km/hr. So we have to convert the values from km/hr to m/s in order to find the solution in terms of metres/seconds.

Hope you understand better. Have a nice day guys!

Q. Sonali invests 15% of her monthly salary in insurance policies. She spends 55% of her monthly salary in shopping and on household expenses. She saves the remaining amount of Rs. 12,750. What is Sonali's monthly income?

Solution:

Let the monthly-salary be X.

Total %-of-amount spent = (15 + 55) = 70% of X.

Remaining amount saved is 30% of X.

Now, 30% of X = 12750. Then 100% of X = ?

X = (12750/30) x 100 = 42,500.

Required answer X = Rs. 42,500. //

Note:-

Amount Spent in Insurance (15% of X) = (15/100) x 42500 = Rs. 6,375.
Amount Spent in Shopping (55% of X) = (55/100) x 42500 = Rs. 23,375.
Amount Saved (30% of X) = (30/100) x 42500 = Rs. 12,750.

Monthly Salary = Rs. (6375 + 23375 + 12750) = Rs. 42,500.

Let length of the train be 'x' metres...
Speed of the train = 60km/hr(given)
Time = 9seconds(given)

refer the formulas for train problems...

As the time is given in seconds and answers are given in metre(train length) we are in need to convert from km/hr to m/s
km/hr = 1000m/(60min*60sec) = 5/18 m/s

Length of the train(distance covered a post)= speed * time
= (60*(5/18))*9
= (50/3)*9
= 150 m

For the train related formulas,check the READ MORE in Left corner(Important formulas)...

if the start line and finish line are same then the time it will take to cross the line is equal to (the length of the vehicle/speed of the vehicle) that crossed the line.

The train took 9 seconds to cross the same line. It is travelling at the speed of 60 km/hr.

60 km/hr means "it took an hour to travel 60 kms."
60 km/hr = 60 km/1 hr.
= 60,000 m/60 mins.
= 60,000 m/3600 sec.
= 600 m/36 sec.
= 50 m/3 sec = 50/3 m/s.

Let length be (l)

Time taken = length/Speed.
9 sec = (l)metres/(50/3)m/s.
(l) Metres = 9 sec * (50/3) m/s.
(l) = 450/3 metres.
(l) = 150 metres.

The length of the train is 150 metres.

Many time we need to change speed from km/h to mtr/sec or mtr/sec to km/h. In the question, to change a speed from km/h to mtr/sec you have to multiply with 1000 and divide with 3600 and then u get speed in mtr/sec. For eg 90km/hr in mtr/sec?

We need to do 90*1000/3600 and u ll get 25m/s. because we do this mainly on every question. so we prepare ourselves in advance by cutting these two cake to serve immediately. Again same eg. 90k/h to m/s.
90 * 5/18 = 25 m/s.

And yes if we want to change m/s to k/h just multiply with 18/5 and you'll get your speed.
Eg. 25m/s to k/h ----25 * 18/5 = 90 k/h.

When we say a train passes a pole in given time then basically we consider that pole as stationary point (having 0 speed) whose length is zero means actually train crosses its own length in given time frame. If we say a running train passes another train (stationery or running) then we have to consider the total length of two trains crossing each other also we have to consider the relative speed of the trains if both trains are running in same direction then relative speed is the difference of their speed and if both are running in opposite direction then their relative speed is sum of their speed.

According to antenna, which we design we say that frequency is between 1 to 5 Mhz or other think we can define values between 1 to 2 Mhz and can use them for infinite frequencies because if we consider frequency between 1 to 2 MHz then if we see then the output can be
1.1,1.111,1.115677,1.9876,1.11153565.....infinity now. Then why we are using this is because if you increase the value before a point it will have a large change as compared to adding values after the point.

And this is because even if there is a small change in frequency then both signals are uncorrelated to large extent.

Here we can use the formula;

The time taken by train to cross an object (i.e. man, pole, tree etc.)
T = L/S.

where T= time taken by train to cross an object.
L= Length of the train.
S= Speed of Train.

we have, S = 60 km/hr.
S = 60 * 5/18 ('*' symbol used for multiplication)
S = 16.66666 meter/second
T = 9 seconds.

Now, 9 = L/16.66666.
L = 9 * 16.
L = 149.99994~ 150 meter .
Answer = 150 meters.

Given that:

Speed of the Train : 60 km/h.
Crosses pole in Seconds : 9 s.

1 km = 1000 meters.
1 km/h = 60 x 1000 meters.

(i.e,) Distance = 60,000 meters.

1 hour = 60 minutes and 1 min = 60 seconds.
1 hour = 60 x 60,
(i.e,) Time = 3600 s,

Speed of the train = Distance/Time.
= 60000 m/3600 s.
= 600 m/36 s.
= 100 m/6 s.
= 50/3 meters per sec.

Length of train = Speed x Time.
= 50/3 x 9,
= 450/9.
= 150 m.

Therefore, the answer is option(D)

Let length of the train be 'x' metres...
Speed of the train = 60km/hr(given)
Time = 9seconds(given)

Refer the formulas for train problems...

As the time is given in seconds and answers are given in metre(train length) We are in need to convert from km/hr to m/s
km/hr = 1000m/(60min*60sec) = 5/18 m/s

Length of the train(distance covered a post)= speed * time
= (60*(5/18))*9
= (50/3)*9
= 150 m

For the train related formulas,check the READ MORE in Left corner(Important formulas)...