Question : A mixture contains liquid A and B in the ratio 5 : 3, respectively. If 3 litres of liquid B is added to it, the ratio of liquid A to liquid B becomes 7 : 6. What is the quantity of liquid A in the mixture?
Option 1: $7 \frac{2}{3}$ litres
Option 2: $9 \frac{1}{3}$ litres
Option 3: $11 \frac{2}{3}$ litres
Option 4: $13 \frac{1}{3}$ litres
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Correct Answer: $11 \frac{2}{3}$ litres
Solution :
The ratio of liquid A and B = 5 : 3
Quantity of liquid added in B = 3 litres
The ratio of liquid A and B after addition = 7 : 6
Let the quantity of the two liquids A and B be $5x$ and $3x$ respectively.
According to the question,
$\frac{(5x)}{(3x + 3)} = \frac{7}{6}$
$⇒ 30x = 21x + 21$
$⇒ 9x = 21$
$⇒ x = \frac{21}{9} = \frac{7}{3}$
$\therefore$ Quantity of liquid A in mixture $=5 \times \frac{7}{3} = \frac{35}{3} = 11\frac{2}{3}$ litres
Hence, the correct answer is $11\frac{2}{3}$ litres.
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