Two trains travelling in the same direction at 50 km/h and 30 ... | Mathematics MCQ | Examoogle

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MathematicsTime, Speed and Distance

Two trains travelling in the same direction at 50 km/h and 30 km/h cross each other completely in 36 seconds. If the length of the first train is 100 m, what is the length of the second train?

100

120

150

Correct Answer

📐 MA • Math Direct FormulaMathematicsTime, Speed and Distance

Option B

100

Quick Summary:

Calculate relative speed in m/s: $(50 - 30) \times \frac{5}{18} = 20 \times \frac{5}{18} = \frac{100}{18} \text{ m/s}$ . Multiply by time ( $36$ s) to get total distance $200$ m, then subtract the length of the first train ( $100$ m).

📐MAMath SolutionDirect Formula

📋 Given

Speed of first train = 50 km/h, speed of second train = 30 km/h, time taken = 36 seconds, length of first train = 100 m.

🔢 Formula Used

D=Srel×T,Srel=S1−S2D = S_{rel} \times T, \quad S_{rel} = S_1 - S_2D=Srel​×T,Srel​=S1​−S2​

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Forgetting to convert the speed from km/h to m/s or using the sum of speeds instead of the difference when trains move in the same direction.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate Relative Speed

Since both trains are moving in the same direction, subtract their speeds to find the relative speed, then convert to m/s by multiplying with $\frac{5}{18}$ .

Srel=(50−30)×518=20×518=10018 m/sS_{rel} = (50 - 30) \times \frac{5}{18} = 20 \times \frac{5}{18} = \frac{100}{18} \text{ m/s}Srel​=(50−30)×185​=20×185​=18100​ m/s

Calculate Total Distance Covered

The total distance covered during the crossing is equal to the sum of the lengths of both trains. Using $D = S_{rel} \times T$ :

D=10018×36=100×2=200 mD = \frac{100}{18} \times 36 = 100 \times 2 = 200 \text{ m}D=18100​×36=100×2=200 m

Determine Length of the Second Train

Since total distance is the sum of both lengths ( $L_1 + L_2 = 200$ ), and $L_1 = 100$ , find $L_2$ .

L2=200−100=100 mL_2 = 200 - 100 = 100 \text{ m}L2​=200−100=100 m

✅

B is correct because the total distance covered is 200 m, and subtracting the first train's length of 100 m leaves 100 m for the second train.

Core Concepts Used

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Relative Speed Distance-Speed-Time Relationship Unit Conversion

💡 EXAM TIP

Always ensure units are consistent before performing operations. This logic applies to boats in a river (upstream/downstream) as well.

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