Question

If two liquids are mixed in equal volumes, their resultant density is 5g/cc and mixed in equal masses their resultant density is 4.8 g/cc. The ratio of their densities is 2/k. Then k=​

Answer 1

let the densities be  D1​ and D2​

Density=VolumeMass​

Case 1 : Equal Volume

⟹M1​=D1​×V

and

M2​=D2​×V

Density combined =2V(M1​+M2​)​=2(D1​+D2​)​=5

⟹D1​+D2​=10

Case 2 : Equal Masses

⟹V1​=D1​M​

⟹V2​=D2​M​

Density combined  =(M/D1​+M/D2​)2M​=(D+1+D2​)2D1​D2​​=4.8

10D1​×D2​​=2.4

⟹D1​×D2​=24

impliesD1​(10−D1​)=24

⟹−D12​+10D1​=24

⟹D12​−10D1​+24=0

⟹D12​−6D1​−4D1​+24=0

⟹(D1​−6)(D1​−4)=0

Then,

D1​=6 or 4

D2​ are 4&6

D2​D1​​=46​=23​ is not of form k2​

while D2​D1​​=64​=32​=k2​⟹k=3