| A container contains a mixture of two liquids A and B in the ratio of 7: 5. When 9 L of mixture is drawn off and the container is filled with B, the ratio of A and B becomes 7: 9. How many litres of liquid A was contained by the container initially? |
A) 10
B) 20
C) 21
D) 25
Correct Answer: C
Solution :
| Suppose the container initially contains \[7x\]and \[5x\,\,L\]of mixtures A and B, respectively. |
| Quantity of A in mixture left' |
| \[=\left( 7x-\frac{7}{12}\times 9 \right)=\left( 7x-\frac{21}{4} \right)\text{L}\] |
| Quantity of B in mixture left |
| \[=\left( 5x-\frac{5}{12}\times 9 \right)=\left( 5x-\frac{15}{4} \right)\text{L}\] |
| \[\therefore \] \[\frac{\left( 7x-\frac{21}{4} \right)}{\left( 5x-\frac{15}{4} \right)+9}=\frac{7}{9}\] |
| \[\Rightarrow \] \[\frac{28x-21}{20x+21}=\frac{7}{9}\] |
| \[\Rightarrow \] \[252x-189=140x+147\] |
| \[\Rightarrow \] \[112x=336\] |
| \[\Rightarrow \] \[x=3\] |
| \[\therefore \]Quantity of liquid A in the container \[7\times 3=21\,\,\text{L}\] |
You need to login to perform this action.
You will be redirected in
3 sec
