Question

Bombay Express left Delhi for Bombay at $14.30$ hrs traveling at a speed of 60 kmph and Rajdhani Express left Delhi for Bombay on the same day at $16.30$ hrs traveling at a speed of 80 kmph. How far away from Delhi will the two trains meet?
A. $120$ km
B. $360$km
C. $480$km
D. $500$ km

Answer 1

Hint: Suppose the time required by Bombay Express to meet Rajdhani Express after $14.30$hrs is $x$.
The distance at which both trains meet is the same.
Find the distance where two trains meet,
If time is $x$hrs and the speed of Bombay Express is 60 kmph.
Then use the speed formula, Speed=$\dfrac{{Distance}}{{Time}}$ so we can find distance as Distance=speed $ \times $time.
The distance traveled by Rajdhani Express from Delhi to the meeting point is $80 \times $ $x - 2$
Rajdhani Express starts 2 hrs later than Bombay Express.
Equate the distance covered by Bombay Express and the distance covered by Rajdhani Express.

Complete step-by-step solution:
Let the time required by the Bombay Express be the $x$axis.
Considering the speed of Bombay express is 60 kmph and the speed of Rajdhani express is 80 kmph.
Since the Rajdhani Express left Delhi for Bombay after two hrs Bombay Express left Delhi. Therefore, It will take two hours less to meet the Bombay Express.
Time taken for Rajdhani Express to meet Bombay Express is $x - 2$ hrs.
The distance covered by Bombay Express=speed $ \times $ time
The distance covered by Bombay Express=60 $ \times $ x
The distance covered by Rajdhani Express=speed $ \times $ time
The distance covered by Rajdhani Express =80 $ \times $ $x - 2$
The distance covered by Bombay express is the same as the distance covered by Rajdhani Express.
$ \Rightarrow 60x = 80(x - 2)$
$ \Rightarrow 60x = 80x - 160$
$ \Rightarrow 160 = 80x - 60x$
$ \Rightarrow 160 = 20x$
Find the value of $x$,
$ \Rightarrow 160 = 20x$
$ \Rightarrow x = 8$hrs
The distance covered by Bombay Express=60 $ \times $ 8
The distance covered by Bombay Express=480 km
Therefore the two trains will meet $480$km away from Delhi.

Option C is the correct answer.

Note: Another Method :
Suppose two trains meet at $x$ km from Delhi.
The time required by Bombay Express to reach $x$ km=$\dfrac{x}{{60}}$ hrs
The time required by Rajdhani Express to reach $x$ km=$\dfrac{x}{{80}}$ hrs
Since the Rajdhani Express left Delhi for Bombay after two hrs Bombay Express left Delhi. Therefore, It will take two hours less to meet the Bombay Express.
Therefore the equate the time taken by Rajdhani Express and Bombay Express, we add 2 hrs to the time of Rajdhani Express.
$\dfrac{x}{{60}} = \dfrac{x}{{80}} + 2$
Take LCM of the denominator of both the sides of the equation that is LCM of 60 and 80 is 240.
Multiply each side by $240$,
\[ \Rightarrow \dfrac{{240x}}{{60}} = \dfrac{{240x}}{{80}} + 480\]
\[ \Rightarrow 4x = 3x + 480\]
\[ \Rightarrow x = 480\]
Therefore the two trains will meet $480$km away from Delhi.