Question

If two different liquids are mixed with equal volumes there density is 9 g/cc and if the same liquids mixing in the equal masses then density is 8 g/cc find individual densities of two liquids​

Answer 1

Answer:

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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

k

2

.Then K is

Medium

Solution

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Correct option is

B

3

Let the densities be D

1

and D

2

Density=

Volume

Mass

Case 1 : Equal Volume

⟹M

1

=D

1

×V

and

M

2

=D

2

×V

Density combined =

2V

(M

1

+M

2

)

=

2

(D

1

+D

2

)

=5

⟹D

1

+D

2

=10

Case 2 : Equal Masses

⟹V

1

=

D

1

M

⟹V

2

=

D

2

M

Density combined =

(M/D

1

+M/D

2

)

2M

=

(D+1+D

2

)

2D

1

D

2

=4.8

10

D

1

×D

2

=2.4

⟹D

1

×D

2

=24

impliesD

1

(10−D

1

)=24

⟹−D

1

2

+10D

1

=24

⟹D

1

2

−10D

1

+24=0

⟹D

1

2

−6D

1

−4D

1

+24=0

⟹(D

1

−6)(D

1

−4)=0

Then,

D

1

=6 or 4

D

2

are 4&6

D

2

D

1

=

4

6

=

2

3

is not of form

k

2

while

D

2

D

1

=

6

4

=

3

2

=

k

2

⟹k=3

Answer 2

Answer:

Let the specific gravities of the two substances be S1 and S2 , and the density of water at 4∘C be ρ .

So, densities of the substances are S1ρ and S2ρ .

Let V be the volume of each of the substances in the mixture.

So, the total mass of the mixture is (VS1ρ+VS2ρ) .

And, the total volume of the mixture is (V+V)=2V .

So, according to the problem, the specific gravity of the mixture is,

S1+S22=4

or, S1+S2=8 …(1).

Again, let m be the mass of each of the two substances in the mixture.

So, the total mass of the mixture is (m+m)=2m .

And, the total volume of the mixture is (mS1ρ+mS2ρ) .

So, the density of the mixture is,

2mmS1ρ+mS2ρ=2S1S2ρS1+S2

So, according to the problem, the specific gravity of the mixture is,

2S1S2S1+S2=3

or, S1S2=32(S1+S2)=32×8=12

So, (S1−S2)=(S1+S2)2−4S1S2−−−−−−−−−−−−−−−√=(8)2−(4×12)−−−−−−−−−−−−√=4 …(2).

From equation (1) , S1=8−S2,

Putting this value in equation (2) , we get, S2 = 2 .

2 .And, putting this value in either of the equations, we get, S1 = 6 .

$thanks$