Multiple choice

Two pipes can fill a tank in 12 and 20 hours respectively. The pipes are opened simultaneously and it is found that due to permanent leakage in the bottom, 30 minutes extra are taken for the cistern to be filled up. If A and B opens for 5 hours then closed, in what time would the leak empty it? दो पाइप क्रमशः 12 और 20 घंटे में एक टैंक भर सकते हैं। पाइप एक साथ खोले जाते हैं और यह पाया जाता है कि तल में स्थायी रिसाव के कारण, सिस्टर्न को भरने के लिए 30 मिनट अतिरिक्त लगते हैं। यदि A और B 5 घंटे के लिए खुलता है और फिर बंद हो जाता है, तो रिसाव कितने समय में इसे खाली कर देगा?

  1. 75

  2. 72

  3. 70

  4. 71

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Combined rate of A and B: 1/12 + 1/20 = 8/60 = 2/15 tanks per hour. Without leak, time = 15/2 = 7.5 hours. With leak, it takes 7.5 + 0.5 = 8 hours. Leak rate = (1/7.5) - (1/8) = 8/60 - 7.5/60 = 0.5/60 = 1/120 tanks per hour. In 5 hours, A+B fill 5 × (2/15) = 2/3 of tank. Leak empties 2/3 in (2/3) / (1/120) = 80 hours. But wait, the question asks something different. If A and B fill for 5 hours and then close, the leak would empty the full tank in 75 hours (120 × 5/8 = 75). Option A matches.

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