A person travels from city A to city B. If he travels at a speed of 50 km/h, he arrives 1 hour early. If he travels at a speed of…

Question

A person travels from city A to city B. If he travels at a speed of 50 km/h, he arrives 1 hour early. If he travels at a speed of 30 km/h, he arrives 1 hour late. What is the distance (in km) between city A and city B?

1. A. 150 km (Correct answer)
2. B. 120 km
3. C. 200 km
4. D. 180 km

Correct Answer

Option A — 150 km

Detailed Solution & Explanation

The correct answer is 150 km.

Key Points

• The two journeys differ in arrival by 2 hours in total — one hour early against one hour late.
• Let the distance be d. The slower trip takes 2 hours longer than the faster one:
  • d/30 − d/50 = 2
  • (5d − 3d)/150 = 2 → 2d/150 = 2 → d = 150 km

Additional Information

• The commonest slip is using a difference of 1 hour instead of 2; "1 hour early" and "1 hour late" are measured from the same scheduled time, so the gap between the journeys is their sum.
• Check: 150 ÷ 30 = 5 hours and 150 ÷ 50 = 3 hours, a difference of exactly 2 ✓, with the scheduled time being 4 hours.
• The direct formula for this pattern is d = (S₁ × S₂ × total time difference) ÷ (S₁ − S₂) = (50 × 30 × 2) ÷ 20 = 150 km.

प्रश्न (हिन्दी में)

एक व्यक्ति शहर A से शहर B तक यात्रा करता है। यदि वह 50 किमी/घंटा की गति से यात्रा करता है, तो वह 1 घंटा पहले पहुँच जाता है। यदि वह 30 किमी/घंटा की गति से यात्रा करता है, तो वह 1 घंटा देरी से पहुँचता है। शहर A और शहर B के बीच की दूरी (किमी में) क्या है?

1. A. 150 किमी
2. B. 120 किमी
3. C. 200 किमी
4. D. 180 किमी