Question

একটি কাজ A, 10 দিনে, B 12 দিনে এবং C 15 দিনে করতে পারে। তারা একসাথে কাজ শুরু করার 2 দিন পরে A ও কাজ সম্পন্ন হওয়ার 4 দিন আগে C চলে যায়। কাজটি শেষ হতে কতদিন লেগেছিল ?​

Answer 1

Solution :-

→ LCM of 10, 12 and 15 = 60 units = Let total work .

So,

→ Efficiency of A = Total work / Time taken = 60/10 = 6 units / day .

→ Efficiency of B = Total work / Time taken = 60/12 = 5 units / day .

→ Efficiency of C = Total work / Time taken = 60/15 = 4 units / day .

So,

→ Work done by (A + B + C) together in first 2 days = 2 * (6 + 5 + 4) = 2 * 15 = 30 units .

Now, A left the work and C left 4 days before work is completed .

then, we can conclude that, in last 4 days only B completed the work .

So,

→ Work done by B in last 4 days = 4 * 5 = 20 units .

therefore,

→ Remaining work done by (B + C) after A left = 60 - (30 + 20) = 10 units .

So,

→ Time taken by (B + C) to complete remaining work = (10/9) days .

hence,

→ Time taken to finish the total work = 2 days (All three) + (10/9) days (B + C) + 4 days (B) = 6 + (10/9) = 7(1/9) days (Ans.)

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