A) 93 gm
B) 100 gm
C) 150 gm
D) 193 gm
Correct Answer: D
Solution :
RD of alloy \[=\frac{\text{wt}\text{.}\,\text{in}\,\text{air}}{\text{loss}\,\text{in}\,\text{wt}\text{.}}=\frac{210}{12}=17.5\] Let it contain \[{{m}_{1}}\]gram of gold and \[{{m}_{2}}\]gram of copper, \[\therefore \] \[{{m}_{1}}+{{m}_{2}}=210\] Volume of alloy (crown) \[=\frac{210}{17.5}=12\,cc.\] Since, volume \[=\frac{\text{Mass}}{\text{Density}}\text{,}\,\,\therefore \,\frac{{{m}_{1}}}{19.3}+\frac{{{m}_{2}}}{8.5}=12\] or \[\frac{{{m}_{1}}}{19.3}+\frac{210-{{m}_{1}}}{8.5}=12\] or \[\frac{8.5\,{{m}_{1}}+19.3(210-{{m}_{1}})}{164.05}=12\] or \[{{m}_{1}}=193\,\text{gram}\text{.}\] Hence, the correction option is [d].
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