13. A and B are two alloys of gold ...

13. A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7: 2 and 7:11, respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in C will be (a) 5:7 (b) 5:9 (c) 7:5 (d) 9:5

11th - 12th Class
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13. (3) Gold Copper Alloy ( A quad frac{7}{9} quad frac{2}{9} ) Alloy ( B quad frac{7}{18} quad frac{11}{18} ) since, alloys ( A ) and ( B ) are melted in the ratio 1: 1 to make the alloy, therefore in the alloy ( C ). the ratio of gold and copper. [ begin{aligned} left(frac{7}{9} times frac{1}{2}+frac{7}{18} times frac{1}{2}right):left(frac{2}{9} times frac{1}{2}+frac{11}{18} times frac{1}{2}right) &=left(frac{7}{9}+frac{7}{18}right):left(frac{2}{9}+frac{11}{18}right) =& frac{21}{18}: frac{15}{18}=21: 15=7: 5 end{aligned} ]
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