CAT (DILR) PYQs

Bottle $1$ contains a mixture of milk and water in $7: 2$ ratio and Bottle $2$ contains a mixture of milk and water in $9: 4$ ratio. In what ratio of volumes should the liquids in Bottle $1$ and Bottle $2$ be combined to obtain a mixture of milk and water in $3: 1$ ratio?

There are four bottles. It is known that three of these bottles contain only P, while the remaining one contains 80% P and 20% I. What is the minimum number of tests required to definitely identify the bottle containing some amount of I?

Consider three mixtures - the first having water and liquid A in the ratio $1: 2$, the second having water and liquid B in the ratio $1: 3$, and the third having water and liquid $C$ in the ratio $1: 4$. These three mixtures of $A, B,$ and $C$, respectively, are further mixed in the proportion $4:3:2$. Then the resulting mixture has