A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litre

Question

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

Options:

A . 10

B . 20

C . 21

D . 25

Answer: Option C

Suppose the can initially contains 7x and 5x of mixtures A and B respectively

Quantity of A in mixture left = \(\left(7x-\frac{7}{12}\times9\right) liters=\left(7x-\frac{21}{4}\right) liters\)

Quantity of B in mixture left = \(\left(5-\frac{5}{12}\times9\right) liters=\left(5x-\frac{15}{4}\right) liters\)

So, \(\frac{\left(7x-\frac{21}{4}\right)}{\left(5x-\frac{15}{4}\right)+9}=\frac{7}{9}\)

\(\frac{28x-21}{20x+21}=\frac{7}{9}\)

252x - 189 = 140x + 147

112x = 336

x = 3.

So, the can contained 21 litres of A.

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