Question : A vessel contained a solution of acid and water, in which water was 64%. Four litres of the solution was taken out of the vessel and the same quantity of water was added. If the resulting solution contains 30% acid, the quantity (in litres) of the water in the solution, at the beginning of the vessel, was:
Option 1: 11.36
Option 2: 15.36
Option 3: 8.64
Option 4: 12.64
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Correct Answer: 15.36
Solution :
Water in the solution = 64%
Acid in the solution = 100% – 64% = 36%
Acid in the new solution = 30%
Water in the new solution = 100% – 30% = 70%
Let the total solution be $100x$
Water = $64x$
Acid = $36x$
According to the question,
$\frac{{64x - 4 × \frac{64}{100} + 4}}{36x - 4 × \frac{36}{100}} = \frac{7}{3}$
⇒ $\frac{64x + 1.44}{36x - 1.44} = \frac{7}{3}$
⇒ $192x + 4.32 = 252x - 10.08$
⇒ $60x = 14.4$
⇒ $x = 0.24$
Thus, $64x = 64 × 0.24= 15.36$ litres
Hence, the correct answer is 15.36.
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