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 of liquid A was contained by the can initially?
Choose the correct choice from the following choices
A) 10 B) 20 C) 21 D) 25 E) 27
Using the values here might be the most straightforward way for this question.   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.   FYI, the algebraic equations will become:   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) = 7*3= 
<gadget id="calculator">7*3</gadget>
<output>21</output>
21.   ANSWER: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 of liquid A was contained by the can initially?