CAT 2023 Slot 1 Solved Paper

Given that in the final mixture, the ratio of coffee and cocoa is 16:9
Let us assume coffee is 16 units and cocoa is 9 units.
⇒ Initially, there are 25 units of coffee and 0 units of cocoa
Let's say x units of the mixture is removed and replaced with cocoa
$\Rightarrow$ Now, we have $\left(25-\mathit{x}\right)$ coffee and $\mathit{x}$ units of cocoa. $\Rightarrow$ Mixture $\mathit{P}$
Now, if $\mathit{x}$ units of the mixture is removed:
Amount of coffee present $=\left(25-\mathrm{x}\right)-\frac{\left(25-\mathit{x}\right)}{25}\times \mathit{x}$
$\Rightarrow \left(25-\mathit{x}\right)\left(1-\frac{\mathit{x}}{25}\right)=16$
$\Rightarrow {\left(25-\mathit{x}\right)}^2=16\times 25$
$\Rightarrow 25-\mathrm{x}=20\Rightarrow \mathrm{x}=5.$
In mixture $\mathit{P}$, cocoa $=\mathit{x}=5$
In mixture $\mathit{Q}$, cocoa $=9$ units.
⇒ Required ratio = 5:9