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?

Question

There are 187 fruits in total. The ratio of apples to mangoes is \(2 : 3\), and the rest are oranges. After selling 67 apples, 26 mangoes, and half of the oranges, the ratio of the remaining apples to oranges becomes \(1 : 2\). Determine how many unsold fruits remain.

Answer 1

Initial state: 16 units of coffee, 9 units of cocoa. Total units = 25.
A mixture of x units is removed and replaced with cocoa.
After removal, remaining coffee = (25 - x) units.
According to the problem statement:
\((25-x)(1-\frac {x}{25}) = 16\)

\((25-x)\frac {(25-x)}{25} = 16\)
\((25-x)^2 = 25 \times 16\)
\((25-x)^2 = 400\)
\((25-x) = \sqrt {400}\)
\(25-x= 20\)
\(x = 5\)
Final mixture P: 5 units of cocoa.
Initial mixture Q: 9 units of cocoa.
The required ratio is 5:9.

Therefore, the correct option is (D): 5:9.

The Correct Option is D

Solution and Explanation

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