Train Problem (Question)

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Important Train Based Formulas : Click Here

Concept: Two Trains Crossing Each Other : ধাৰণা: দুটা ৰেল পৰস্পৰ অতিক্ৰম কৰা

When two trains cross each other, the total distance covered is the sum of their lengths. যেতিয়া দুটা ৰেলে পৰস্পৰ অতিক্ৰম কৰে, তেতিয়া মুঠ দূৰত্ব হ’ল দুয়ো ৰেলৰ দৈৰ্ঘ্যৰ যোগফল।

Total distance = L₁ + L₂ : মুঠ দূৰত্ব = L₁ + L₂

Relative Speed (Opposite Direction) : আপেক্ষিক গতি (বিপৰীত দিশত)

If two trains move in opposite directions, their relative speed is the sum of their speeds. যদি দুটা ৰেল বিপৰীত দিশত চলে, তেন্তে আপেক্ষিক গতি হ’ল দুয়ো গতিৰ যোগফল।

Relative Speed = S₁ + S₂ : আপেক্ষিক গতি = S₁ + S₂

Time Formula: সময়ৰ সূত্ৰ

Time = L1 + L2 / S1 + S2 সময় = L1 + L2 / S1 + S2​​

Given Data : প্ৰদত্ত তথ্য

Speed of Train 1 (S₁) = 110 m/s : Train 1 ৰ গতি = 110 মি/ছে

Speed of Train 2 (S₂) = 140 m/s : Train 2 ৰ গতি = 140 মি/ছে

S1 + S2 = 110 + 140 = 250 m/s 

Case 1: Numerical Problem : গণিতীয় উদাহৰণ

Length of Train 1 (L₁) = 400 m : Train 1 ৰ দৈৰ্ঘ্য = 400 মি

Length of Train 2 (L₂) = 600 m : Train 2 ৰ দৈৰ্ঘ্য = 600 মি

Solⁿ : সমাধান

L1 + L2 = 400 + 600 = 1000 m L

Time = 1000 / 250 = 4 seconds

Final Answer : চূড়ান্ত উত্তৰ : Time taken by the two trains to cross each other = 4 seconds : দুটা ৰেলে পৰস্পৰ অতিক্ৰম কৰিবলৈ লোৱা সময় = ৪ ছেকেণ্ড

 Key Exam Tips (SSC / HSLC) : পৰীক্ষাৰ গুৰুত্বপূর্ণ টিপছ

• Crossing each other → Add lengths : অতিক্ৰম কৰা → দৈৰ্ঘ্য যোগ


• Opposite direction → Add speeds : বিপৰীত দিশ → গতি যোগ


• Same direction → Subtract speeds : একেটা দিশ → গতি বিয়োগ


• km/h to m/s conversion → × 5/18  : km/h ৰ পৰা m/s লৈ → × 5/18

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Q.  A train of length X m, moving at a speed of 59 m/sec, crosses a railway platform of length 279 m in 9 seconds. Find the value of X.

A. 262  B. 256  C. 252  D. 253

Solution

Distance covered in 9 seconds: $$59\times 9=531\text{ m}$$

While crossing a platform:

$$\text{Total distance }=\text{Train length }+\text{Platform length}$$ $$531=X+279$$

                                                                       X = 531−279 = 252 m​

Ans: C. 252 m

Trick: 59 × 9 − 279 = 531 − 279 = 252

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Train : Bridge Problem

Q. A person drives a car at a speed of 21 km/h and crosses a bridge in 18 minutes. What is the length of the bridge ?

A. 15.2 km  B. 4.7 km   C. 2.5 km   D. 6.3 km

Solution

Formula: Distance = Speed × Time

Convert minutes into hours: 18 minutes = 18/60 = 0.3 hour

Now,

Distance = 21 × 0.3 = 6.3 km

Ans: (D) 6.3 km

Trick

Distance = Speed × Time (Always remember to convert minutes into hours before calculating.)

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