A train 400 meter long overtook a man walking along the line in the same direction at a speed of 5 km/hr and passed him in 40 seconds. The train reached the station in 20 minutes after it had passed the man. In what time did the man reach the station?

Shohan

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2025-01-04 04:42

1 Answers

Shohan

প্রশ্নে বলা হচ্ছে যে, 400 মিটার দীর্ঘ একটি ট্রেন একই দিকে 5kmph বেগে চলমান একজন লোককে 40 সেকেন্ডে অতিক্রম করে। লোকটিকে অতিক্রম করার 20 মিনিট পরে ট্রেনটি স্টেশনে পৌঁছাল। লোকটি কখন স্টেশনে পৌছাবে? ট্রেনের বহুল ব্যবহৃত Shortcut সূত্রের মাধ্যমেও এই অঙ্কের সমাধান সম্ভব ।

আমরা জানি, $t = \frac{d_{1} + d_{2}}{v_{1} - v_{2}}$ [ট্রেন ও লোকটি একই দিকে গতিশীল বলে]

$\Rightarrow 40 = \frac{400 + 0}{\frac{(v_{1} - 5) 5}{18}}$ [এখনে, t = 40; ট্রেনের দৈর্ঘ্য d₁ = 400 মিটার; লোকটির দৈর্ঘ্য ট্রেনের সাপেক্ষে, d₂ = 0; v₁= ট্রেনের বেগ; v₂ = লোকটির বেগ]

$\Rightarrow (v_{1} - 5) = \frac{400 \times 18}{40 \times 5}$

$\Rightarrow v_{1} - 5 = 36$

∴ v₁= 36 + 5 = 41

অর্থাৎ ট্রেনটির গতিবেগ 41 kmph. [ $∵$ 20 মিনিট $= \frac{1}{3}$ ঘণ্টা]

এখন, এই $\frac{41}{3} k m$ পথ লোকটি 5 kmph বেগে কত সময়ে অতিক্রম করবে সেটাই বের করতে হবে।

আমরা জানি, প্রয়োজনীয় সময় = দূরত্ব / বেগ $= \frac{\frac{41}{3}}{5} = \frac{41}{3} \times \frac{1}{5} = \frac{41}{15}$ = 2 ঘণ্টা 44 মিনিট (answer)

উল্লেখ্য $\frac{41}{15}$ ঘণ্টাকে কিভাবে 2 ঘণ্টা 44 মিনিটে আনা হলো তা লক্ষ্য করুনঃ

অতএব, $\frac{41}{15} = 2 \frac{11}{15}$ ঘণ্টা

এখানে, 1 ঘণ্টা = 60 মিনিট

∴ $\frac{11}{15}$ ঘণ্টা $= \frac{60 \times 11}{15}$ = 44 মিনিট

12 views Answered 2024-12-14 13:31

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