రైలు A పొడవు 260 మీటర్లు. ఇది 160 మీటర్ల పొడవు గల ప్లాట్&zwnj;... | Mathematics MCQ (తెలుగు) | Examoogle

MathematicsTime, Speed and Distance

రైలు A పొడవు 260 మీటర్లు. ఇది 160 మీటర్ల పొడవు గల ప్లాట్‌ఫారాన్ని 28 సెకన్లలో దాటుతుంది. రైలు B పొడవు 340 మీటర్లు. ఇది ఒక స్థిరంగా ఉన్న వ్యక్తిని 20 సెకన్లలో దాటుతుంది. రెండు రైళ్లు సమాంతర సరళ పట్టాలపై స్థిర వేగాలతో ప్రయాణిస్తున్నాయి. ఒకే దిశలో ప్రయాణిస్తున్నప్పుడు, వేగవంతమైన రైలు నెమ్మదిగా ఉన్న రైలును పూర్తిగా అధిగమించడానికి పట్టే సమయం (సెకన్లలో) ఎంత?

250

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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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