A) 10
B) 20
C) 21
D) 25
Correct Answer: C
Solution :
Let the mixture of two liquids be 7x and 5x. |
If 9 L of mixture be drawn, |
Then, liquid A, |
\[7x-9\times \frac{7}{7+5}=7x-\frac{63}{12}=7x-\frac{21}{4}L\] |
and liquid B,\[5x-9\times \frac{5}{7+5}=5x-\frac{45}{12}=5x-\frac{15}{4}\] |
When 9 L mixture is mixed in B, then the quantity |
\[B=\left( 5x-\frac{15}{4}+9 \right)L\] |
According to the given condition,\[\frac{\left( 7x-\frac{21}{4} \right)}{\left( 5x-\frac{15}{4}+9 \right)}=\frac{7}{9}\] |
\[\Rightarrow \] \[63x-\frac{189}{4}=35x-\frac{105}{4}+63\] |
\[\Rightarrow \] \[63x-35x=\frac{-105}{4}+63+\frac{189}{4}\] |
\[\Rightarrow \] \[28x=\frac{-105+252+189}{4}\] |
\[\Rightarrow \] \[28x=\frac{336}{4}=84\]\[\Rightarrow \]\[x=\frac{84}{28}=3\] |
\[\therefore \] Quantity of \[A=7x=7\times 3=21\,\,L\] |
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