A can contains a mixture of 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 liter W of liquid A was contained by the can initially?  Pick one.
A) 10
B) 20
C) 21
D) 25
E) 27
As A:B::7:5 ---&gt; only option C is a multiple of 7 and hence it is a good place to start. Also A:B::7:5 means that , A = (712)*Total and B = (5/12)*Total   If A = 21 , B = 15 ---&gt; remove 9 litres ---&gt; you remove (7/12)*9 of A ---&gt; A remaining = 21-(7/12)*9 = 63/4   Similarly, for B, you remove (5/12)*9 ---&gt; B remaining = 15 - (5/12)*9 = 45/4 and then add 9 more litres of B ---&gt; 9+45/4 = 81/4   Thus A/B (final ratio) = (45/4)/(81/4) = 7:9 , the same as the final ratio mentioned in the question.   Hence C is the correct answer.   A/B = 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9), where 7x and 5x are initial quantities of A and B respectively.   Thus, 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9) ---&gt; giving you x=3. Thus A (original) W= 7*3 = 21.21
<result>C</result>
A can contains a mixture of 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 liter W of liquid A was contained by the can initially?