CAT 2025 Slot 2 QA Question 2: A mixture of coffee and cocoa, $16\%$ of which is coffee, costs Rs $240$ per kg. Another mixture of coffee and cocoa, of which $36\%$ is coffee, costs Rs $320$ per kg. If a new mixture of coffee and c

Question

A mixture of coffee and cocoa, $16\%$ of which is coffee, costs Rs $240$ per kg. Another mixture of coffee and cocoa, of which $36\%$ is coffee, costs Rs $320$ per kg. If a new mixture of coffee and c

Accepted Answer

Let the prices of coffee and cocoa be $C$ and $K$ rupees per kg, respectively.

$0.16 C + 0.84 K = 240$
$0.36 C + 0.64 K = 320$
Subtracting, $0.20 C - 0.20 K = 80$
$\Rightarrow C - K = 400$

Using the first equation, we get $K = 176$ and $C = 576$.

Let $p$ be the fraction of coffee in the new mixtu