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

10

20

21

25

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#### Solution

**21Explanation:**Let the quantity of liquid A and B be 7x and 5x, respectively.

Then, as per the question `(12x-9 7/12)/(12x-9 5/12+9)=7/9`

⇒ `(7x-21/4)/(5x-15/4+9)=7/9`

⇒ `(28x-21)/(20x-15+36)=7/9`

⇒ `252x-189=140x+147`

⇒ `112x=336⇒x=3`

∴ Initial amount of liquid A= 7x = 7 x 3 = 21 L

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