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Length_A = Length_B/2. Speed_A:Speed_B = 2:3. A crosses 100m platform in 5 seconds; B crosses 100m platform in 6 seconds. Find length of B.

1. 450 m
2. 800 m
3. 600 m
4. 900 m

Correct answer: 800 m

Solution

L_A=b/2. Speed_A=(b/2+100)/5. Speed_B=(b+100)/6. Speed_A/Speed_B=2/3: [(b/2+100)/5]/[(b+100)/6]=2/3. 6(b/2+100)=10(b+100)/3... → 5(b+100)=(b/2+100)×(15/2). Solving: 5(b+100)=(b+100)/(2)×(15/2)... Let me redo: speed_A/speed_B = [(b/2+100)/5]/[(b+100)/6] = 6(b/2+100)/[5(b+100)] = 2/3. So 18(b/2+100)=10(b+100) → 9b+1800=10b+1000 → b=800. ✓

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