Question : A vessel contains a solution of two liquids A and B in the ratio 5 : 3. When 10 litres of the solution is taken out and replaced by the same quantity of B, the ratio of A and B in the vessel becomes 10 : 11. The quantity (in litres) of the solution, in the vessel was ______.
Option 1: 42
Option 2: 48
Option 3: 52
Option 4: 44
Correct Answer: 42
Solution :
Given,
The ratio of the solution of two liquids = 5 : 3
When 10 litres of the solution is taken out and replaced by the same quantity of B, the ratio of A and B in the vessel becomes 10 : 11
The ratio of two liquids A and B is = $5x : 3x$
According to the question,
$\frac{5x−\frac{5}{8}×10}{3x−\frac38×10+10}=\frac{10}{11}$
⇒ $\frac{\frac{40x−50}{8}}{\frac{24x−30+80}{8}}=\frac{10}{11}$
⇒ $\frac{4x – 5}{24x + 50} = \frac{1}{11}$
⇒ $44x - 55 = 24x + 50$
⇒ $44x - 24x = 50 + 55$
⇒ $20x = 105$
⇒ $x = \frac{105}{20}$
⇒ $x = \frac{21}{4}$
Total quantity of liquids = $\frac{21}{4} × 8$ = 42 litres
Hence, the correct answer is 42 litres.
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