A train runs between two stations A and B, while going from A to B, its…
2013
A train runs between two stations A and B, while going from A to B, its average speed is 90 km/hr and while coming back from B to A its average speed is 110 km/hr. The average speed during the whole journey is
- A.
95 km/hr
95 किमी/घण्टा
- B.
99 km/hr
99 किमी/घण्टा
- C.
100 km/hr
100 किमी/घण्टा
- D.
102 km/hr
102 किमी/घण्टा
Attempted by 5 students.
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Correct answer: B
To find the average speed for the entire journey, we use the formula for average speed when distances are equal: 2ab/(a+b), where a and b are the speeds for the two halves of the journey.
Here, a = 90 km/hr and b = 110 km/hr.
Average speed = 2 × 90 × 110 / (90 + 110) = 19800 / 200 = 99 km/hr.
Note: The average speed is not the arithmetic mean (90 + 110)/2 = 100 km/hr, because the train spends more time at the lower speed.
हिन्दी उत्तर: पूरी यात्रा के लिए औसत चाल ज्ञात करने के लिए, जब दूरी समान हो, तो हम सूत्र 2ab/(a+b) का उपयोग करते हैं, जहाँ a और b दोनों भागों की चाल हैं।
यहाँ, a = 90 किमी/घण्टा और b = 110 किमी/घण्टा।
औसत चाल = 2 × 90 × 110 / (90 + 110) = 19800 / 200 = 99 किमी/घण्टा।
ध्यान दें: औसत चाल अंकगणितीय माध्य (90 + 110)/2 = 100 किमी/घण्टा नहीं है, क्योंकि ट्रेन कम चाल पर अधिक समय बिताती है।