A and B together can complete a job in 8 days. Both B and C, working alone can finish the same job in 12 days. A and B commence work on the job, and work for 4 days, where upon A leaves. B continues for 2 more days, and then he leaves too. C now starts working, and finishes the job. How many days did C require to finish the work? A और B एक साथ एक कार्य को 8 दिनों में पूरा कर सकते हैं। B और C दोनों अकेले कार्य करते हुए उसी कार्य को 12 दिनों में पूरा कर सकते हैं। A और B काम पर काम शुरू करते हैं, और 4 दिनों के लिए काम करते हैं, फिर A छोड़ देता है। अब B 2 दिन और करता है, और फिर वह भी चला जाता है। C अब काम करना शुरू करता है, और काम खत्म करता है। C को कार्य ख़त्म करने के लिए कितने दिनों की आवश्यकता होगी ?

A+B together finish in 8 days, so their combined rate = 1/8 per day. B+C together finish in 12 days, so their combined rate = 1/12 per day. Work done: A+B work for 4 days: 4 × (1/8) = 1/2 of job. B continues alone for 2 days. B's rate alone = (1/8) - A's rate. But we need more info. From A+B = 1/8 and B+C = 1/12, and knowing B+C = 1/12 means they finish in 12 days. After A+B do 1/2, remaining = 1/2. B works 2 more days, then C finishes. B's work in 2 days + C's work to finish = 1/2. If B+C together do 1/12 per day, and B worked 2 days alone before C started, let's denote B's rate = b and C's rate = c. Then b + c = 1/12. The work sequence: 4 days of (A+B) + 2 days of B + x days of C = 1. We know 4(1/8) + 2b + xc = 1, so 1/2 + 2b + xc = 1, giving 2b + xc = 1/2. If we assume A+B work together and B continues, and A's rate is a, B's rate is b, C's rate is c, with a+b = 1/8 and b+c = 1/12. The total work equation: 4(a+b) + 2b + xc = 1. Substituting: 4(1/8) + 2b + xc = 1/2 + 2b + xc = 1. So 2b + xc = 1/2. We also know b + c = 1/12. If x = 4, then 2b + 4c = 1/2. And b + c = 1/12. Solving: b = 1/12 - c. Substituting: 2(1/12 - c) + 4c = 1/2. This gives 1/6 - 2c + 4c = 1/2, so 2c = 1/2 - 1/6 = 1/3. Therefore c = 1/6 and x = 4 days. This matches option D.