Question

Two trains start at the same time from Aligarh and Delhi and move towards each other at the rate of 16km/hr and 21
km/hr respectively. When they meet, it is found that one train has travelled 60 km more than the other. The distance
between two stations is:
A.504 km
B.445 km
C.444 km
D.440km​

Answer 1

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✤ Required Answer:

✒ GiveN:

• Two trains started their journey from Aligarh and Delhi at speed 16 km/hr and 21 km/hr
• When they meet, one train have travelled 60 km more than other.

✒ To Find:

• Find the distance between the stations...?

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✤ How to solve?

The above question can be solved by using pair of linear equations in two variables. We will frame two equations and then, solve it by using suitable method like substitution or elemination method.

⏏ For this Q., we also need to know the relation between Distance, Time and speed.

$\large{ \boxed{ \sf{Speed = \frac{Distance}{time} }}}$

This relation can be modified in any way to find the Required quantity like distance, time or speed.

☃️ So, let's solve this question.

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✤ Solution:

Let,

• Distance travelled by train A = x
• And, distance travelled by train B = y

According to question,

• Distance travelled by one train is 60 km more than distance travelled by second train.
• Let Distance travelled by train A is more than train B, because nothing is mentioned in Q.

So,

➝ x = y + 60

➝ x - y = 60

Then,

Speed of x > speed of y

• Speed of x = 21 km/hr
• And speed of y = 16 km/hr

Also,

• The time taken to travelled so far to meet each other is also equal.

We can write the above formula as,

$\large{ \because{ \boxed{ \sf{Time = \dfrac{Distance}{Speed} }}}}$

➝ Time taken by Train A = Time taken by Train B

➝ tA = tB

➝ x / 21 = y / 16

Cross multiplying,

➝ 16x = 21y

➝ 16x - 21y = 0............(2)

Multiplying eq. (1) with 16,

➝ 16(x - y) = 60 × 16

➝ 16x - 16y = 960......(1)

Subtracting eq. (1) from eq. (2),

➝ 16x - 16y - (16x - 21y) = 960

➝ 16x - 16y - 16x + 21y = 960

➝ 5y = 960

➝ y = 192 km

Substituting value of y in eq. (1),

➝ x - 192 = 60

➝ x = 252 km

✏ Refer to the attachment...

Distance between the two stations,

➝ x km + y km

➝ 192 km + 252 km

➝ 444 km

Answer - 444 km

⚘$\large{ \gray{ \underline{ \underline{ \bf{Option \: C}}}}}$

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