Question

An alloy of gold and copper
(densities 20gm/cm' and
10gm/cmº respectively) weighs
30 gm in air and 28 gm. In water
(density = 1 gm/cm). Find the
ratio of volumes of gold and
copper respectively.​

Answer 1

$\textbf{Given:}$

$\textsf{An alloy of gold and copper(densities 20gm/cubic.cm and}$

$\textsf{10gm/cubic.cm respectively) weighs 30 gm in air and 28 gm}$

$\textbf{To find:}$

$\textsf{Ratio of volumes of gold and copper}$

$\textbf{Solution:}$

$\underline{\textsf{Formula used:}}$

$\boxed{\mathsf{Density=\dfrac{Mass}{Volume}}}$

$\underline{\mathsf{Gold:}}$

$\mathsf{Density=20\;gm/cm^3}$

$\mathsf{Mass=30\;gm}$

$\mathsf{Volume=\dfrac{Mass}{Density}}$

$\implies\mathsf{V_1=\dfrac{30}{20}}$

$\underline{\mathsf{Copper:}}$

$\mathsf{Density=10\;gm/cm^3}$

$\mathsf{Mass=28\;gm}$

$\mathsf{Volume=\dfrac{Mass}{Density}}$

$\implies\mathsf{V_2=\dfrac{28}{10}}$

$\mathsf{Now,}$

$\mathsf{\dfrac{V_1}{V_2}=\dfrac{\dfrac{30}{20}}{\dfrac{28}{10}}}$

$\mathsf{\dfrac{V_1}{V_2}=\dfrac{\dfrac{3}{2}}{\dfrac{14}{5}}}$

$\mathsf{\dfrac{V_1}{V_2}=\dfrac{3}{2}{\times}\dfrac{5}{14}}$

$\mathsf{\dfrac{V_1}{V_2}=\dfrac{15}{28}}$

$\implies\boxed{\mathsf{V_1\;:\;V_2=15\;:\;28}}$

Answer 2

Answer:

An alloy of gold and copper(densities 20gm/cubic.cm and

\textsf{10gm/cubic.cm respectively) weighs 30 gm in air and 28 gm}10gm/cubic.cm respectively) weighs 30 gm in air and 28 gm

\textbf{To find:}To find:

\textsf{Ratio of volumes of gold and copper}Ratio of volumes of gold and copper

\textbf{Solution:}Solution:

\underline{\textsf{Formula used:}}

Formula used:

\boxed{\mathsf{Density=\dfrac{Mass}{Volume}}}

Density=

Volume

Mass

\underline{\mathsf{Gold:}}

Gold:

\mathsf{Density=20\;gm/cm^3}Density=20gm/cm

3

\mathsf{Mass=30\;gm}Mass=30gm

\mathsf{Volume=\dfrac{Mass}{Density}}Volume=

Density

Mass

\implies\mathsf{V_1=\dfrac{30}{20}}⟹V

1

=

20

30

\underline{\mathsf{Copper:}}

Copper:

\mathsf{Density=10\;gm/cm^3}Density=10gm/cm

3

\mathsf{Mass=28\;gm}Mass=28gm

\mathsf{Volume=\dfrac{Mass}{Density}}Volume=

Density

Mass

\implies\mathsf{V_2=\dfrac{28}{10}}⟹V

2

=

10

28

\mathsf{Now,}Now,

\mathsf{\dfrac{V_1}{V_2}=\dfrac{\dfrac{30}{20}}{\dfrac{28}{10}}}

V

2

V

1

=

10

28

20

30

\mathsf{\dfrac{V_1}{V_2}=\dfrac{\dfrac{3}{2}}{\dfrac{14}{5}}}

V

2

V

1

=

5

14

2

3

\mathsf{\dfrac{V_1}{V_2}=\dfrac{3}{2}{\times}\dfrac{5}{14}}

V

2

V

1

=

2

3

×

14

5

\mathsf{\dfrac{V_1}{V_2}=\dfrac{15}{28}}

V

2

V

1

=

28

15

\implies\boxed{\mathsf{V_1\;:\;V_2=15\;:\;28}}⟹

V

1

:V

2

=15:28