260 மீ நீளமுள்ள இரயில் A, 160 மீ நீளமுள்ள ஒரு நடைமேடையை 28 விந... | Mathematics MCQ (தமிழ்) | Examoogle

MathematicsTime, Speed and Distance

260 மீ நீளமுள்ள இரயில் A, 160 மீ நீளமுள்ள ஒரு நடைமேடையை 28 விநாடிகளில் கடக்கிறது. 340 மீ நீளமுள்ள இரயில் B, நிலையாக நிற்கும் ஒரு மனிதனை 20 விநாடிகளில் கடக்கிறது. இரண்டு இரயில்களும் இணையான நேர் தண்டவாளங்களில் சீரான வேகத்தில் பயணிக்கின்றன. இரண்டு இரயில்களும் ஒரே திசையில் செல்லும்போது, வேகமாகச் செல்லும் இரயில் மெதுவாகச் செல்லும் இரயிலை முழுமையாக முந்திச் செல்ல எடுத்துக்கொள்ளும் நேரம் (விநாடிகளில்) எவ்வளவு?

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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