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

A and B bought lands on the Moon from an eStore, both with the same diameter but A’s land is square-shaped, and B’s land is circular. What is the ratio of the areas of their respective lands?

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.

	Mutual fund A	Mutual fund B	Mutual fund C
Person 1	₹10,000	₹20,000	₹20,000
Person 2	₹20,000	₹15,000	₹15,000

List I		List II
A.	Duplicate of ratio 2: 7	I.	25:30
B.	Compound ratio of 2: 7, 5:3 and 4:7	II.	4:49
C.	Ratio of 2: 7 is same as	III.	40:147
D.	Ratio of 5: 6 is same as	IV.	4:14

The Correct Option is D

Solution and Explanation

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