Question

A can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of mixture is drawn off and the can is filled with B, the ratio of A and B becomes 7:9. Litres of liquid A contained by the can initially was:

• A. 10
• B. 20
• C. 21
• D. 25
• E. None of these

Answer 1

The correct option is C 21

Let the quantity initially of liquid A be 7x litre
$\therefore$ Let the quantity initially of liquid B be 5x litre
Quantity of A after 9 litres mixture drawn
$=7x-\frac{21}{4}=\frac{28x-21}{4}litres$
Quantity of B after 9 litres mixture drawn and adding 9 litres of B $=5x+\frac{21}{4}=\frac{20x+21}{4}$
$\therefore \frac{(28x-21)}{4}:\frac{20x+21}{4}=\frac{7}{9}$
$\Rightarrow (252-140)x=189+147$
$\Rightarrow x=\frac{336}{112}=3$
The required quantity of A = 7x = 21 litres.