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Ratio and Proportion

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Question : 44 of 112

Marks: +1, -0

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 :

$5 : 7$
$5 : 9$
$7 : 5$
$9 : 5$

Solution:

Concept:

Find the fraction of gold and copper in each alloy per unit quantity, then add them and simplify the ratio.

Explanation:

Take 1 unit of alloy A: gold =

\frac{7}{9}

, copper =

\frac{2}{9}

.

Take 1 unit of alloy B: gold =

\frac{7}{18}

, copper =

\frac{11}{18}

.

Total gold =

\frac{7}{9} + \frac{7}{18} = \frac{14+7}{18} = \frac{21}{18} = \frac{7}{6}

.

Total copper =

\frac{2}{9} + \frac{11}{18} = \frac{4+11}{18} = \frac{15}{18} = \frac{5}{6}

.

Ratio of gold to copper in alloy C =

\frac{7}{6} : \frac{5}{6} = 7 : 5

.

Answer:

7 : 5

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