| A can contains a mixture of two liquids A and B in the ratio 7: 5.When 9 L of mixture are 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 by the can initially? |
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, |
| \[\frac{7x-\frac{21}{4}}{5x-\frac{15}{4}+9}=\frac{7}{9}\]\[\Rightarrow \]\[\frac{28x-21}{20x-15+36}=\frac{7}{9}\] |
| \[\Rightarrow \] \[\frac{28x-21}{20x+21}=\frac{7}{9}\]\[\Rightarrow \]\[\frac{4x-3}{20x+21}=\frac{1}{9}\] |
| \[\therefore \] \[x=3\] |
| Original quantity of liquid \[A=7x=7\times 3=21\,\,L\] |
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