Multiple choice

A, B and C can complete a work in 30 days by working together. If the efficiency of A and C are twice the efficiency of B and the efficiency of A and B is thrice the efficiency of C. In how many days A will complete the work? A, B और C एक साथ कार्य करके किसी कार्य को 30 दिनों में पूरा कर सकते हैं । यदि A और C की कार्यक्षमता B की कार्यक्षमता की दुगनी है और A और B की कार्यक्षमता C की कार्यक्षमता की तीन गुनी है, तो A काम को कितने दिनों में समाप्त कर लेगा ?

  1. 72 days/दिन

  2. 40 days/दिन

  3. 30 days/दिन

  4. 20 days/दिन
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A Correct answer
Explanation

Let A, B, C have efficiencies a, b, c. Combined rate: a + b + c = 1/30 work/day. Given: a + c = 2b and a + b = 3c. Substituting: a + c = 2b means a + c + b = 3b, so 1/30 = 3b, giving b = 1/90. From a + b = 3c: a + 1/90 = 3c. Also a = 2b - c = 2/90 - c. Solving gives a = 1/72, so A takes 72 days alone. Option B (40 days) is incorrect. Option C (30 days) is the combined time, not A's alone. Option D is a miscalculation.

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