ট্রেন A এর দৈর্ঘ্য 260 মি এবং এটি 160 মি দৈর্ঘ্যের একটি প্ল্যা... | Mathematics MCQ (বাংলা) | Examoogle

MathematicsTime, Speed and Distance

ট্রেন A এর দৈর্ঘ্য 260 মি এবং এটি 160 মি দৈর্ঘ্যের একটি প্ল্যাটফর্ম 28 সেকেন্ডে অতিক্রম করে। ট্রেন B এর দৈর্ঘ্য 340 মি এবং এটি 20 সেকেন্ডে একজন স্থির ব্যক্তিকে অতিক্রম করে। উভয় ট্রেন সমান্তরাল সোজ ট্র্যাকে স্থির গতিতে চলে। একই দিকে চলার সময় দ্রুতগতির ট্রেনটি ধীরগতির ট্রেনটিকে সম্পূর্ণরূপে অতিক্রম করতে কত সময় (সেকেন্ডে) নেয়?

250

320

360

300

Correct Answer

📐 MA • Math Direct FormulaMathematicsTime, Speed and Distance

300

Quick Summary:

Calculate speeds separately: $S_A = (260+160)/28 = 15$ m/s, $S_B = 340/20 = 17$ m/s. Relative speed = $17-15 = 2$ m/s. Time = sum of lengths / relative speed = $(260+340)/2 = 300$ seconds.

📐MAMath SolutionDirect Formula

📋 Given

Train A: length = 260 m, crossing 160 m platform in 28 s. Train B: length = 340 m, crossing a man in 20 s.

🔢 Formula Used

Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}Speed=TimeDistance​, Relative Speed=SB−SA\text{Relative}\ \text{Speed} = S_B - S_ARelative Speed=SB​−SA​, Time=Total LengthRelative Speed\text{Time} = \frac{\text{Total}\ \text{Length}}{\text{Relative}\ \text{Speed}}Time=Relative SpeedTotal Length​

⚡ Exam Hall Shortcut / Speed Trick

Calculate speeds separately: $S_A = (260+160)/28 = 15$ m/s, $S_B = 340/20 = 17$ m/s. Relative speed = $17-15 = 2$ m/s. Time = sum of lengths / relative speed = $(260+340)/2 = 300$ seconds.

⚠️ Common Student Trap / Pitfall

Students often add the lengths of both trains when crossing a man or a platform, but you must only add the lengths of the two trains when they are overtaking each other.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate speed of Train A

Train A covers its own length plus the platform length. Total distance = $260 + 160 = 420$ m. $S_A = 420 / 28 = 15$ m/s.

SA=260+16028=15 m/sS_A = \frac{260 + 160}{28} = 15 \text{ m/s}SA​=28260+160​=15 m/s

Calculate speed of Train B

Train B crosses a stationary man, so it covers only its own length. $S_B = 340 / 20 = 17$ m/s.

SB=34020=17 m/sS_B = \frac{340}{20} = 17 \text{ m/s}SB​=20340​=17 m/s

Calculate relative speed and time to overtake

Since trains move in the same direction, relative speed is the difference of speeds. Total distance to cover is the sum of both train lengths: $260 + 340 = 600$ m.

Time=260+34017−15=6002=300 s\text{Time} = \frac{260 + 340}{17 - 15} = \frac{600}{2} = 300 \text{ s}Time=17−15260+340​=2600​=300 s

✅

D is correct because the faster train (Train B) overtakes Train A in 300 seconds.

Core Concepts Used

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Relative Speed Train Problems Uniform Motion

💡 EXAM TIP

This concept is fundamentally identical to circular track problems where the faster runner laps the slower runner by the circumference of the track.

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