A can contains a mixture of two liquids A and B in the ratio of 7: 5. When 9 L of mixture is drained 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 in the can initially? |
[SSC (10+2)2012] |
A) 10
B) 20
C) 21
D) 25
Correct Answer: C
Solution :
Let the original quantity be \[12x\,\,L.\] |
In 9 L of the mixture, |
Liquid A \[=\frac{7}{12}\times 9=\frac{21}{4}\,\,L\] |
Liquid B \[=\frac{5}{12}\times 9=\frac{15}{4}L\] |
According to the question, |
\[\frac{7x-\frac{21}{4}}{5x-\frac{15}{4}+9}=\frac{7}{9}\] |
\[\Rightarrow \] \[\frac{28x-21}{20x-15+36}=\frac{7}{9}\] |
\[\Rightarrow \] \[\frac{4x-3}{20x+21}=\frac{1}{9}\]\[\Rightarrow \]\[x=3\] |
\[\therefore \]Original quantity of liquid\[A=7x=21\,\,L\] |
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