Question

A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off , the ratio A and B becomes 7: 9. How many litres of liquid A was contained by the can initially ?

• A. 10
• B. 20
• C. 21
• D. 25

Answer 1

The correct option is C 21

Step:1 :Let the Can contain 7x and 5x liters of mixture A and B respectively .Quantity of mixture drawn of = 9 liter
$\therefore quantityofAinmixtureleft=(7x-\frac{7}{12}\times 9)=(7x-\frac{21}{4})liter$
$\therefore quantityofBinmixtureleft=(5x-\frac{5}{12}\times 9)=(5x-\frac{15}{4})liter$
Step ii : Since the mixture is in the ratio $7:9$
$\frac{(7x-\frac{21}{4})}{(5x-\frac{15}{4})+9}=\frac{7}{9}$
$\Rightarrow \frac{28x-21}{20x+21}=\frac{7}{9}$
$\Rightarrow 252x-189=140x+147$
$\Rightarrow 112x=336$
$\Rightarrow x=3$
$\therefore QuantityofliquidA,containedinthecaninitially=7\times 3=21liter$