Multiple choice

Pipes A and B can fill a tank in 16 hours and 24 hours, respectively, and pipe C alone can empty the full tank in x hours. All the pipes were opened together at 10.30 a.m., but C was closed at 2:30 p.m. If the tank was full at 8:30 p.m. on the same day, then what is the value of x ? पाइप A और B एक टैंक को क्रमशः 16 घंटे और 24 घंटे में भर सकते हैं, और पाइप C अकेले पूर्ण टैंक को x घंटे में खाली कर सकता है। सभी पाइपों को एक साथ सुबह 10.30 बजे खोला गया, लेकिन C को दोपहर 2:30 बजे बंद कर दिया गया। अगर टैंक उसी दिन रात 8:30 बजे भर गया था।, तो x का मान क्या है?

  1. 64

  2. 48

  3. 45

  4. 96

  5. None of these इनमें से कोई नहीं

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's rate: 1/16 tank/hour, B's rate: 1/24 tank/hour, C's rate: -1/x tank/hour (emptying). 10:30 a.m. to 2:30 p.m. = 4 hours with all three open. 2:30 p.m. to 8:30 p.m. = 6 hours with only A and B. Work in first 4 hours: 4(1/16 + 1/24 - 1/x) = 4(5/48 - 1/x). Work in next 6 hours: 6(5/48) = 5/8. Total: 4(5/48 - 1/x) + 5/8 = 1. Solving: 20/48 + 30/48 - 4/x = 1, giving -4/x = -1/24, so x = 96.