A vessel contains liquids A and B in a ratio of 5 : 3. If 16 litres of the mixture is removed and the same quantity of liquid B is added, the ratio becomes 3 : 5. What quantity does the vessel hold?
40 liters
Let the vessel hold 8k litres, with A = 5k and B = 3k.
Removing 16 litres of the mixture removes A: 16×(5/8)=10 and B: 16×(3/8)=6, leaving A = 5k-10, B = 3k-6. Adding 16 litres of B gives new B = 3k-6+16 = 3k+10.
New ratio: (5k-10)/(3k+10) = 3/5 ⟹ 5(5k-10) = 3(3k+10) ⟹ 25k-50 = 9k+30 ⟹ 16k = 80 ⟹ k = 5.
Total capacity = 8k = 40 litres.
Hence, this is the correct answer.
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