A 150 m long train moving at 54 km/h crosses a platform in 20 ... | Mathematics MCQ | Examoogle

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MathematicsTime, Speed and Distance

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A 150 m long train moving at 54 km/h crosses a platform in 20 seconds. What is the length of the platform?

100 m

150 m

200 m

250 m

Correct Answer

📐 MA • Math Direct FormulaMathematicsTime, Speed and Distance

Option B

150 m

Quick Summary:

Convert speed directly: $54 \times \frac{5}{18} = 15$ m/s. Then, calculate total distance as $15 \times 20 = 300$ m and subtract the train length ( $300 - 150 = 150$ m).

📐MAMath SolutionDirect Formula

📋 Given

Length of train = 150 m, Speed of train = 54 km/h, Time taken to cross = 20 s

🔢 Formula Used

D=S×TD = S \times TD=S×T

⚡ Exam Hall Shortcut / Speed Trick

Convert speed directly: $54 \times \frac{5}{18} = 15$ m/s. Then, calculate total distance as $15 \times 20 = 300$ m and subtract the train length ( $300 - 150 = 150$ m).

⚠️ Common Student Trap / Pitfall

Failing to convert the speed from km/h to m/s, which leads to incorrect units during the calculation.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Convert speed to m/s

To maintain consistent units, convert the speed from km/h to m/s using the conversion factor $\frac{5}{18}$ .

S=54×518=15 m/sS = 54 \times \frac{5}{18} = 15 \text{ m/s}S=54×185​=15 m/s

Calculate total distance

The total distance covered while crossing the platform is the sum of the train length ( $L_{T}$ ) and the platform length ( $L_{P}$ ). Using the formula $D = S \times T$ :

LT+LP=15×20=300 mL_{T} + L_{P} = 15 \times 20 = 300 \text{ m}LT​+LP​=15×20=300 m

Find platform length

Subtract the length of the train from the total distance to find the length of the platform.

LP=300−150=150 mL_{P} = 300 - 150 = 150 \text{ m}LP​=300−150=150 m

✅

B is correct because the calculated length of the platform is 150 m.

Core Concepts Used

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Unit conversion Relative distance Time-Speed-Distance relationship

💡 EXAM TIP

This concept of total distance (Object 1 + Object 2) is identical to problems involving trains crossing bridges or tunnels, and relates to relative velocity in Physics kinematics.

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