Two pipes A and B together can fil a cistern in 18 hours. Ratio of efficiency of pipe A and pipe B is 2: 3. Find in what time cistern can be fully filled if pipes A and B are opened alternatively in a way that A alone is opened for first three hours and then B alone is opened for next 1 hour till the whole cistern get filled? दो पाइप A और B मिलकर एक टंकी को 18 घंटे में भर सकते हैं। पाइप A और पाइप B की दक्षता का अनुपात 2:3 है। यदि पाइप A और B को वैकल्पिक रूप से इस तरह से खोला जाता है कि पहले तीन घंटे के लिए अकेले A को खोला जाता है और फिर B अकेले अगले 1 के लिए खोला जाता है तो इस तरह टंकी कितने घंटे में पूरी भर जायेगी?

A+B together fill in 18 hours, so combined rate = 1/18 per hour. Efficiency ratio 2:3 means A's rate = 2/5 * 1/18 = 1/45 per hour, B's rate = 3/5 * 1/18 = 1/30 per hour. Alternating pattern: A for 3 hours, B for 1 hour, repeated. Each 4-hour cycle: A fills 3/45 = 1/15, B fills 1/30. Total per cycle = 1/15 + 1/30 = 1/10. After 7 cycles (28 hours): tank at 7/10. A for 3 more hours: + 1/15 = 7/10 + 1/15 = 21/30 + 2/30 = 23/30. B for 1 hour: + 1/30 = 24/30 = 4/5. A for 3 hours: + 1/15 = 4/5 + 1/15 = 12/15 + 1/15 = 13/15. B for 1 hour: + 1/30 = 26/30 + 1/30 = 27/30 = 9/10. Continue until total reaches 1... Actually need to track more carefully. Let me restart: Each cycle adds 1/10. After 9 cycles (36 hours): 9/10 filled. A for 3 hours: + 1/15 = 9/10 + 1/15 = 27/30 + 2/30 = 29/30. B for 1 hour: + 1/30 = 30/30 = 1. Total = 36 + 3 + 1 = 40 hours. Option A is correct.