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A train travelling 25 km an hour leaves Aligarh at 9a.m. and another train travelling 35 km and hour starts at 2 p.m. in the same direction. How many km from Aligarh will they be together?
\[
  \left( a \right)750km \\
  \left( b \right)437\dfrac{1}{2}km \\
  \left( c \right)417\dfrac{1}{2}km \\
  \left( d \right)407\dfrac{1}{2}km \\
 \]

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Last updated date: 14th Jul 2024
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Answer
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Hint: In this question, we use the concept of relative speed. Relative speed is defined as the speed of a moving object with respect to another. When two objects are moving in the same direction, relative speed is calculated as their difference.

Complete step-by-step answer:

Speed of the first train is 25km/h and speed of the second train is 35km/h.
Now, the first train leaves the Aligarh station at 9a.m. and travels by 2p.m. so the first train takes 5 hours.
Distance cover by first train in 5 hours,
$
  {\text{Distance = }}\left( {{\text{speed of first train}}} \right) \times \left( {{\text{time taken by first train}}} \right) \\
   \Rightarrow {\text{Distance = }}25 \times 5 \\
   \Rightarrow {\text{Distance = }}125km \\
$
Distance covered by the first train in 5 hours is 125km.
Now, relative speed of two trains $ = \left( {35 - 25} \right)km/h = 10km/h$
Now we find time taken by second train will meet the first train,
$
  {\text{Time taken}} = \dfrac{{{\text{Distance covered by first train }}}}{{{\text{Relative speed}}}} \\
   \Rightarrow {\text{Time taken}} = \dfrac{{125}}{{10}} \\
   \Rightarrow {\text{Time taken}} = 12.5{\text{hours}} \\
$
Now the distance from Aligarh when both the trains are together,
$
   = \left( {{\text{Time taken}}} \right) \times \left( {{\text{Speed of second train}}} \right) \\
   = 12.5 \times 35 = 437.5km = 437\dfrac{1}{2}km \\
$
So, the correct option is (b).

Note: Whenever we face such types of problems we use some important points. First we find the distance covered by the first train with respect to the second train then find relative speed by using the concept of relative motion and also find time. So, we will get the required answer.