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 ⇒ Now, we have (25−x) coffee and x units of cocoa. ⇒ Mixture P Now, if x units of the mixture is removed: Amount of coffee present =(25−x)−
(25−x)
25
×x ⇒(25−x)(1−
x
25
)=16 ⇒(25−x)2=16×25 ⇒25−x=20⇒x=5. In mixture P, cocoa =x=5 In mixture Q, cocoa =9 units. ⇒ Required ratio = 5:9