Answer
Verified
419.7k+ views
Hint: Assume the time required for Bombay express for meeting as ‘x’ and then use the concept that both the trains will meet at same distance and same time. Then use the formula of distance as \[Distance=speed\times time\] to get the distances of both the trains and then equate these values to get the values to get the value of ‘x’. Put this value of ‘x’ in one of the formulae of distance to get the final answer.
Complete step-by-step answer:
To solve the given question we will write the given data first, therefore,
Speed of Bombay Express = 60 kmph ……………………………………………. (1)
Speed of Rajdhani Express = 80 kmph …………………………………………… (2)
As the Bombay Express is left at 14.30 hrs therefore we will assume that after ‘x’ hrs it will meet the Rajdhani Express. Therefore,
Time required for Bombay Express for meeting = x hrs ………………………………. (3)
As Rajdhani Express is left at 16.30 hrs i.e. two hrs late than Bombay express therefore it should take two hours less to meet the Bombay Express. Therefore,
Time required for Rajdhani Express for meeting = (x – 2) hrs …………………………. (4)
Now, As the two trains are leaving from the same station and they are travelling the same distance therefore when they will meet each other at that time they should have covered the equal distance therefore we can write, at the time of meeting,
Distance covered by Bombay Express = Distance covered by Rajdhani Express …………………… (5)
Now to proceed further in the solution we should know the formula of distance in terms of speed and time which is given below,
Formula:
\[Distance=speed\times time\]
By using the above formula we can write,
Distance covered by Bombay Express = (Speed of Bombay Express) \[\times \](Time required for Bombay Express
for meeting)
If we put the value of equation (1) and equation (3) in the above equation we will get,
Distance covered by Bombay Express = 60 \[\times \] x ………………………………………………. (6)
Also we can write,
Distance covered by Rajdhani Express = (Speed of Rajdhani Express) \[\times \] (Time required for Rajdhani
Express for meeting)
If we put the values of equation (2) and equation (4) in the above equation we will get,
Distance covered by Rajdhani Express = 80 \[\times \] (x – 2) ……………………………………. (7)
If we put the value of equation (6) and equation (7) in equation (5) we will get,
60 \[\times \] x = 80 \[\times \] (x – 2)
Therefore, 60x = 80x – 160
Therefore, 60x – 80x = - 160
Therefore, - 20x = - 160
Therefore, \[x=\dfrac{160}{20}\]
Therefore, x = 8 hrs
If we put the above value in equation (6) we will get,
Distance covered by Bombay Express = 60 \[\times \] 8
Therefore distance covered by Bombay Express = 480 km.
If we compare the above equation with equation (5) we will get,
Distance covered by Bombay Express = Distance covered by Rajdhani Express = 480 km.
Therefore the two trains will meet 480 km away from the Delhi stations.
Therefore the correct answer is option (c).
Note: There is a chance that you will get confused while taking the time required for Rajdhani express for meeting but do remember that the trains are going to meet at same time and same distance and for that Rajdhani express should take less time as it is leaving late.
Complete step-by-step answer:
To solve the given question we will write the given data first, therefore,
Speed of Bombay Express = 60 kmph ……………………………………………. (1)
Speed of Rajdhani Express = 80 kmph …………………………………………… (2)
As the Bombay Express is left at 14.30 hrs therefore we will assume that after ‘x’ hrs it will meet the Rajdhani Express. Therefore,
Time required for Bombay Express for meeting = x hrs ………………………………. (3)
As Rajdhani Express is left at 16.30 hrs i.e. two hrs late than Bombay express therefore it should take two hours less to meet the Bombay Express. Therefore,
Time required for Rajdhani Express for meeting = (x – 2) hrs …………………………. (4)
Now, As the two trains are leaving from the same station and they are travelling the same distance therefore when they will meet each other at that time they should have covered the equal distance therefore we can write, at the time of meeting,
Distance covered by Bombay Express = Distance covered by Rajdhani Express …………………… (5)
Now to proceed further in the solution we should know the formula of distance in terms of speed and time which is given below,
Formula:
\[Distance=speed\times time\]
By using the above formula we can write,
Distance covered by Bombay Express = (Speed of Bombay Express) \[\times \](Time required for Bombay Express
for meeting)
If we put the value of equation (1) and equation (3) in the above equation we will get,
Distance covered by Bombay Express = 60 \[\times \] x ………………………………………………. (6)
Also we can write,
Distance covered by Rajdhani Express = (Speed of Rajdhani Express) \[\times \] (Time required for Rajdhani
Express for meeting)
If we put the values of equation (2) and equation (4) in the above equation we will get,
Distance covered by Rajdhani Express = 80 \[\times \] (x – 2) ……………………………………. (7)
If we put the value of equation (6) and equation (7) in equation (5) we will get,
60 \[\times \] x = 80 \[\times \] (x – 2)
Therefore, 60x = 80x – 160
Therefore, 60x – 80x = - 160
Therefore, - 20x = - 160
Therefore, \[x=\dfrac{160}{20}\]
Therefore, x = 8 hrs
If we put the above value in equation (6) we will get,
Distance covered by Bombay Express = 60 \[\times \] 8
Therefore distance covered by Bombay Express = 480 km.
If we compare the above equation with equation (5) we will get,
Distance covered by Bombay Express = Distance covered by Rajdhani Express = 480 km.
Therefore the two trains will meet 480 km away from the Delhi stations.
Therefore the correct answer is option (c).
Note: There is a chance that you will get confused while taking the time required for Rajdhani express for meeting but do remember that the trains are going to meet at same time and same distance and for that Rajdhani express should take less time as it is leaving late.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE