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Two cars, X and Y, start from points 360 km apart and travel at constant speeds. If they move towards each other, they meet in 4 hours. If they move in the same direction, they meet in 12 hours. What is the speed of car X? (Assume X is the faster car.)

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Two cars, X and Y, start from points 360 km apart and travel at constant speeds. If they move towards each other, they meet in 4 hours. If they move in the same direction, they meet in 12 hours. What is the speed of car X? (Assume X is the faster car.)

दो कारें X और Y, 360 किमी की दूरी पर स्थित बिंदुओं से चलती हैं और उनकी गति स्थिर है। यदि वे एक-दूसरे की ओर चलती हैं, तो 4 घंटे में मिलती हैं। यदि वे एक ही दिशा में चलती हैं, तो 12 घंटे में मिलती हैं। कार X की गति ज्ञात कीजिए। (मान लें X तेज़ कार है।)

Options / विकल्प

A. 60 km/h ✅

B. 75 km/h

C. 45 km/h

D. 90 km/h

Answer / उत्तर

✅ 60 km/h

Solution / समाधान

Shortcut Trick / शॉर्टकट ट्रिक

When moving towards each other:

X+Y=3604X + Y = \frac{360}{4} X+Y=90 km/hX + Y = 90 \text{ km/h}

When moving in the same direction:

X−Y=36012X - Y = \frac{360}{12} X−Y=30 km/hX - Y = 30 \text{ km/h}

Adding the two equations:

(X+Y)+(X−Y)=90+30(X+Y)+(X-Y)=90+30
2X=1202X=120
X=60 km/hX=60 \text{ km/h}

Alternative Method / वैकल्पिक विधि

X=(X+Y)+(X−Y)2X=\frac{(X+Y)+(X-Y)}{2} X=90+302X=\frac{90+30}{2} X=1202X=\frac{120}{2} X=60 km/hX=60 \text{ km/h}

Final Answer / अंतिम उत्तर

60 km/h\boxed{60 \text{ km/h}}

✅ Correct Answer / सही उत्तर: 60 km/h

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