Multiple choice

P and Q together can do a piece of work in 12 days. Q and R together do it in 15 days. If P's efficiency is twice that of R, then the days required for Q alone to finish the work is- / P और Q एक कार्य को एकसाथ मिलकर 12 दिन में कर सकते हैं। Q और R इसे 15 दिन में करते हैं। यदि P की कार्यक्षमता R की दोगुनी है, तो Q को कार्य को अकेले पूरा करने के लिए आवश्यक दिनों की संख्या है-

  1. 15 days / दिन

  2. 20 days / दिन

  3. 30 days / दिन

  4. 60 days / दिन
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B Correct answer
Explanation

Let P=2x, Q=y, R=x (P is twice as efficient as R). P+Q = 1/12 work/day, Q+R = 1/15 work/day. Substituting: 2x+y = 1/12 and y+x = 1/15. Subtracting: x = 1/12 - 1/15 = (5-4)/60 = 1/60. So y = 1/15 - 1/60 = 4/60 - 1/60 = 3/60 = 1/20. Q's rate = 1/20, so Q alone takes 20 days. Verification: P=1/30, R=1/60, Q=1/20. P+Q=1/30+1/20=5/60=1/12 ✓, Q+R=1/20+1/60=4/60=1/15 ✓.

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