If Arif works alone he will take 20 more hours to complete a task than if he works with Babu to complete the task. If Babu work alone, he will take 5 more hours to complete the task than if he works with Arif to complete the task. What is the ratio of the time taken by Arif to than taken by Babu if each of them works alone to complete the task?

Question: If Arif works alone he will take 20 more hours to complete a task than if he works with Babu to complete the task. If Babu work alone, he will take 5 more hours to complete the task than if he works with Arif to complete the task. What is the ratio of the time taken by Arif to than taken by Babu if each of them works alone to complete the task?Solution:ধরি আরিফ ও বাবু কাজটি করে x ঘণ্টায় আরিফ একা কাজটি করে (x + 20) ঘণ্টায়বাবু একা কাজটি করে (x + 5) ঘণ্টায়প্রশ্নমতে,{1/(x + 20)} + {1/(x + 5)} = 1/x⇒ 1/(x + 20) = (1/x) - {1/(x + 5)}⇒ 1/(x + 20) = (x + 5 - x)/(x2 + 5x)⇒ 1/(x + 20) = 5/(x2 + 5x)⇒ x2 + 5x = 5x + 100⇒ x2 = 100 ∴ x = 10আরিফ একা কাজটি করে (10 + 20) ঘণ্টা = 30 ঘণ্টায় বাবু একা কাজটি করে (10 + 5) ঘণ্টা = 15 ঘণ্টায়আরিফ ও বাবুর কাজের সময়ের অনুপাত = 30 : 15 = 2 : 1