SSC Sample Paper Mock Test-16 SSC CGL Tear-II Paper-1

A can contains a mixture of two liquids A and B in the ratio 7 : 5 When 9 L of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9 L of liquid contained by the can initially was

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 \[A=7x=7\times 3=21\,\,L\]