Question

At what time will the train reach city X from city Y.
a. The train crosses another train at an equal length of $200$metres and runs in opposite directions in $15$ seconds.
b. The train leaves city Y at $7:15\,\,a.m$ for city X situated at a distance of
c. The $200$ metres long train crosses a signal pole in $10$ seconds.
Which of the above statements give the answer:
A.(a) only
B.(b) only
C.(c) only
D.(b) and (c) only
E.All (a) ,(b) and (c) are required.

Answer 1

Here we are given with the problem in a statement form. Any statement problem can be converted to a mathematical form which is then solved to get the required solution. So, here we will first try to convert the given statements to mathematical form then we will be using formula relating to speed and distance to find the required solution.
Formula used:
$Distance = Speed \times Time$

Complete answer:
We have to read all the statements carefully and decide which statement gives us the answer.
From the first statement, we get the length of the train which is $200m$ . And we cannot use the rest of the information for calculating the speed of the train because the two trains can run at the same speed.
In the second statement, we can calculate the time taken by formula
$\dfrac{{distance}}{{speed}}$
By putting the values we get:
$\dfrac{{558}}{{72}}hrs$
On simplifying the term we have:
$\Rightarrow \dfrac{{31}}{4} = 7hrs45\min$
Now in the third statement, we can calculate the speed with the formula
$Speed = \dfrac{{Dis\tan ce}}{{time}}$
By substituting the values we get:
$\Rightarrow \dfrac{{200}}{{10}}m/\sec = 20m/\sec$
We can convert the value in km/hr also. So the new equation is:
$\Rightarrow 20 \times \dfrac{{18}}{5} = 72km/hr$
Therefore we can see that only the first stamen has redundant info while comparing the other two statements.

Hence the correct option is D. (b) and (c) only.

Note:
We should always be careful regarding the data in the question and hat needs to be calculated. Therefore, based on the requirement and by observing all the necessary information that is already available in the question we gather the information and then create an equation, or we can apply another method such as the unitary method whichever is applicable, then we solve the problem and then verify the answer by putting the value in the problem and see whether we get the same answer or not.