Multiple choice

If two liquids are mixed in equal volumes, their resultant density is 5 gr/cc and mixed in equal masses their resultant density is 4.8 g/cc . The ratio of their densities is $\frac{2}{k}$ .Then K is

  1. 1

  2. 3

  3. 4

  4. 5
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B Correct answer
Explanation

Let densities be d1, d2. Equal volumes: (d1+d2)/2 = 5 => d1+d2 = 10. Equal masses: 2/(1/d1 + 1/d2) = 4.8 => 2*d1*d2 / (d1+d2) = 4.8 => d1*d2 = 24. Roots of x^2 - 10x + 24 = 0 are 4 and 6. Ratio d1/d2 = 4/6 = 2/3 or 6/4 = 3/2. Given ratio is 2/k. If 2/3, k=3. If 3/2, k=4/3.

AI explanation

Using the equal volumes mixture rule, the average of the two densities is 5, which means the sum of the densities is 10. Using the equal masses mixture rule, the harmonic mean of the densities is 4.8, so 2 multiplied by the product of the densities divided by their sum of 10 equals 4.8, making the product of the densities 24. Solving the system where the sum is 10 and the product is 24 gives the ratio of the densities as 2/3, which means K equals 3.

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