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X and Y are two stations 500 km apart. A train starts from X and moves toward Y at 20 km/hr another train starts from Y at the same times and moves toward X at 30 km/hr. How far from X will they cross each other?
- a)200 km.
- b)30 km.
- c)120 km.
- d)40 km.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
X and Y are two stations 500 km apart. A train starts from X and moves...
Suppose they meet x km from X
⇒ 30x = 10000 − 20x
∴ x = 200 km.
⇒ 30x = 10000 − 20x
∴ x = 200 km.
Most Upvoted Answer
X and Y are two stations 500 km apart. A train starts from X and moves...
Problem Statement:
X and Y are two stations 500 km apart. A train starts from X and moves toward Y at 20 km/hr another train starts from Y at the same times and moves toward X at 30 km/hr. How far from X will they cross each other?
Solution:
Let's assume that after time 't' hours, the two trains meet at a point 'P' which is at a distance 'd' km from station X. Now, let's find the value of 'd'.
Distance travelled by train starting from X in 't' hours = 20t km
Distance travelled by train starting from Y in 't' hours = 30t km
Total distance travelled by both trains when they meet at point 'P' = distance between stations X and Y = 500 km
Therefore, we can write the following equation:
20t + 30t = 500
Simplifying the equation, we get:
50t = 500
t = 10 hours
Now, we can find the distance 'd' travelled by the train starting from station X in 10 hours as follows:
d = 20t = 20 x 10 = 200 km
Therefore, the two trains will cross each other at a distance of 200 km from station X.
Final Answer:
Option (a) 200 km.
X and Y are two stations 500 km apart. A train starts from X and moves toward Y at 20 km/hr another train starts from Y at the same times and moves toward X at 30 km/hr. How far from X will they cross each other?
Solution:
Let's assume that after time 't' hours, the two trains meet at a point 'P' which is at a distance 'd' km from station X. Now, let's find the value of 'd'.
Distance travelled by train starting from X in 't' hours = 20t km
Distance travelled by train starting from Y in 't' hours = 30t km
Total distance travelled by both trains when they meet at point 'P' = distance between stations X and Y = 500 km
Therefore, we can write the following equation:
20t + 30t = 500
Simplifying the equation, we get:
50t = 500
t = 10 hours
Now, we can find the distance 'd' travelled by the train starting from station X in 10 hours as follows:
d = 20t = 20 x 10 = 200 km
Therefore, the two trains will cross each other at a distance of 200 km from station X.
Final Answer:
Option (a) 200 km.
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