Two pipes A and B can fill a water tank in 72 and 108 minutes respectively. If both the pipes work alternately then how long will it take to fill the tank? (A start to fill the tank first ) दो पाइप A और B क्रमशः 72 और 108 मिनट में एक पानी के टैंक को भर सकते है| यदि दोनों पाइपो को एकान्तर क्रम में खोला जाये तो तो कितने समय में टैंक भर जाएगा? ( पहले A शुरू भरना करता है )

Pipe A fills in 72 minutes (rate: 1/72 per minute), Pipe B in 108 minutes (rate: 1/108 per minute). Working alternately starting with A: Cycle of 2 minutes fills (1/72 + 1/108) = 5/216 of tank. After 86 minutes (43 complete cycles), tank is 43 × 5/216 = 215/216 full. Remaining 1/216 needs Pipe A (who works 87th minute): (1/72)t = 1/216 gives t = 1/3 minute = 20 seconds. Total time = 86 + 1/3 = 86.33 minutes. The key is finding complete cycles first, then handling the remainder.