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 and the same amount is again removed from P and replaced with the same amount of cocoa powder to form a mixture Q. If the ratio of coffee and cocoa in Q=16:9. Then the ratio of coca in with P:Q is?

• A. 1:3
• B. 4:9
• C. 1:2
• D. 5:9

Answer 1

Answer: (D)

5:9

Answer 2

Let, coffee comprises 16 units and cocoa comprises 9 units.
There are 25 units of coffee and 0 units of cocoa.
Let, x units of the mixture are removed and replaced with cocoa.
If x units of the mixture are removed then (25 - x) units of coffee left.
According to the question,
$(25-x)(1-\frac {x}{25}) = 16$

$(25-x)\frac {(25-x)}{25} = 16$
$(25-x)^2 = 25 \times 16$
$(25-x)^2 = 400$
$(25-x) = \sqrt {400}$
$25-x= 20$
$x = 5$
Now, in mixture P, cocoa = 5 units
And, in mixture Q, cocoa = 9 units
The required ratio = 5:9

So, the correct option is (D): 5:9