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UGC-NET-Paper1

Maths

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The speed of an electric train is 25% more than that of a steam engine train. What is the time taken by the electric train to cover a distance which the steam engine train takes 4 hours 25 minutes to cover?

1. 3 1/10 hr
2. 3 11/15 hr
3. 3 11/12 hr
4. 3 8/15 hr

एक इलेक्ट्रिक ट्रेन की गति स्टीम इंजन ट्रेन की गति से 25% अधिक है। इलेक्ट्रिक ट्रेन को वह दूरी तय करने में कितना समय लगेगा, जिसे तय करने में स्टीम इंजन ट्रेन को 4 घंटे 25 मिनट लगते हैं?

1. 3 1/10 घंटे
2. 3 11/15 घंटे
3. 3 11/12 घंटे
4. 3 8/15 घंटे
This Question came in
UGC-NET-Sociology-16-January-2025-Shift-1-Q16
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Detailed Explanation & Answer
### Step 1: Define Variables
Let the speed of the steam engine train be **S**.
The speed of the electric train is **25% more**, so its speed = **1.25S**.
Time taken by the steam engine = **4 hours 25 minutes** = **4 + 25/60** = **4 5/12 hours**.

### Step 2: Compute Time for the Electric Train
Since time is inversely proportional to speed:

Time taken by the electric train = (Time taken by steam engine × Speed of steam engine) / Speed of electric train

= (4 5/12 × S) / (1.25S)
= (4 5/12) / 1.25
= (53/12) ÷ (5/4)
= (53/12) × (4/5)
= (53 × 4) / (12 × 5)
= 212 / 60
= **3 8/15 hours**

### Final Answer:
**(4) 3 8/15 hr**
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