Aptitude - Problems on Trains - Discussion

Another approach by looking at answers, in question, 27 come first and 17 come later so in answer bigger number will come first and smaller later, that option is "B" only, so we can find answer without going for actual calculation.

Total distance / total speed = total time.

This is the simple solution (X + Y) = relative speed.

Trains comes towards each other.

Guys!

Difference between the 23s and 27s is 4 and,

Difference between the 23s and 17s is 6 of other train.

So, the ratio is 4 and 6.

Short-cut : Alligation method.


27 17
23
6 4

= 6 : 4 means 3 : 2 => Answer.

Here is the formula when two trains crosses each other,

s1 + s2 = l1 + l2/time.

According to the problem.
x + y = (27x + 17y) /23.
27x + 17y = (x + y)23.
x/y = 3/2.

This can be easily done by the method of allegations.
27 17
23

(23-17) : (27-23)
6 : 4
3 : 2

Or by weighted average,

S1/S2 = (23-17)/(27-23)

=> 3/2 and that is the required ratio.

Guys, there is an easy way to understand this question.

Let us consider the SPEED of Train'A' and Train'B' as X and Y.

Trains moving in opposite direction which crosses a man standing on the platform signifies the TIME of trains taken to cross the man which are 27s and 17s respectively, not the time taken by trains to cross each other(given separately in the question).

Therefore,

DISTANCE of the trains taken to cross the man = SPEED * TIME.
D (TRAIN A)= X * 27.
D (TRAIN B)= Y * 17.

So, now we know that DISTANCE(LENGTH)covered by the trains and its SPEED(mentioned above).

From this, it is understood that its time to find out the TIME take by the trains.
But the time has already given;

TIME = DISTANCE/SPEED.

23 = 27x + 17y /x + y.
Cross multiply 23 (x + y) = 27x + 17y.

Bring all like terms on same sides; So,

23x + 23y = 27x + 17y.
23x - 27x = 17y - 23y.
- 4x = - 6y.

Since both the sides have a negative sign, it will automatically get deleted)ie, 4x = 6y .

Now its time to form the answer in ratio form.
Ratio forms when one digit is divided by the other digit, always remember NUMERATOR should be greater than DENOMINATOR.

4x = 6y .
(Bring all like terms on same sides).

Then, x/y = 6/4.
= 3/2 ie, 3 : 2.

Answer = 3 : 2.

An alternative answer:

27 - 23 = 4.
27 - 17 = 6.

Take the square root of both 6 and 4
=> 3:2.

In very simple method.

27 17

23

6 : 4
...................
3:2
..................

By using mixed alligation method.

The speeds of trains should be added because they are moving in opposite direction.

-------------> man < ----------------.

The speeds of both trains contributing to finish it in 23 seconds.