pot contains 81 litres of pure milk 13 of liters of the milk is replaced by the same amount of water. Again 13 of the mixture is replaced by that amount of water. Find the ratio of milk and water in the new mixture.

Shohan

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2025-01-04 04:42

1 Answers

Shohan

প্রশ্নে বলা হচ্ছে, একটি পাত্রে 81 লিটার দুধ রয়েছে। পাত্রের $\frac{1}{3}$ অংশ দুধকে পানি দ্বারা Replace করা হলো। এরপর আরো একবার $\frac{1}{3}$ অংশ পানি মিশ্রিত দুধকে পানি দ্বারা Replace করা হলো। নতুন মিশ্রণে দুধ ও পানির অনুপাত কত?

Shortcut সূত্র ব্যবহার করে এবং জটিলতা পরিহার করে অঙ্কটি করলে দ্রুত সমাধানে পৌঁছে যাওয়া সম্ভব।

এবার সূত্রটি দেখুনঃ $x {(1 - \frac{y}{x})}^{n}$

এখানে, x = মোট দুধের পরিমাণ = 81 লিটার;

y = যতটুকু দুধ সরিয়ে পানি Replace করা হয়েছে $= (81 এ র \frac{1}{3})$ = 27 লিটার;

n = কাজটি কতবার করা হয়েছে = 2 বার ।

অতএব, দুইবার পানি দ্বারা দুধকে Replace করার পর তাতে দুধ আছে

$81 {(1 - \frac{27}{81})}^{2} = {(1 - \frac{1}{3})}^{2} = 81 \times {(\frac{2}{3})}^{2} = 81 \times \frac{4}{9}$ = 36 লিটার

∴ ঐ মিশ্রণে পানি আছে = 81 – 36 = 45 লিটার

অতএব, নতুন মিশ্রণে দুধ : পানি = 36 : 45 = 4 : 5 (answer)

4 views Answered 2024-12-14 13:31

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