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Q.

Two metals are mixed together in equal volumes to form an alloy of specific gravity 4. When equal masses of the same two metals are mixed together, the specific gravity of the along is 3. The specific gravity of each metal is

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a

2 and 6

b

2 and 4

c

4 and 6

d

4 and 8

answer is B.

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Detailed Solution

Equal volumes

= \frac{ρ_{1} + ρ_{2}}{2} = 4 \Rightarrow ρ_{1} + ρ_{2} = 8 \to (1)

Equal masses $= \frac{2 ρ_{1} ρ_{2}}{ρ_{1} + ρ_{2}} = 3 \Rightarrow ρ_{1} ρ_{2} = 12$

${(ρ_{1} - ρ_{2})}^{2} = {(ρ_{1} + ρ_{2})}^{2} - 4 ρ_{1} ρ_{2}$

$= 8^{2} - 4 \times 12 = 16$

$ρ_{1} - ρ_{2} = 4 \to (2)$

Add equation (1) & (2)

$ρ_{1} = 6 g/c .c ρ_{2} = 2 g/c .c$

Specific gravities are 2 and 6.

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Two metals are mixed together in equal volumes to form an alloy of specific gravity 4. When equal masses of the same two metals are mixed together, the specific gravity of the along is 3. The specific gravity of each metal is