CAT 2023 Slot 1 QA Question 11: A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture P and replaced with the sa

Question

A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture P and replaced with the sa

Accepted Answer

Let the fraction removed and replaced each time be r. The fraction of coffee left after one replacement is $1-r$.

After the second replacement, the coffee fraction in Q is
$(1-r)^2$

In Q, coffee : cocoa = 16 : 9, so the coffee fraction is $\dfrac{16}{25}$.
$(1-r)^2 = \dfrac{16}{25}$
$1-r = \dfrac{