A and B are two alloys of copper and tin prepared by mixing metals in the ratio of 4 : 3 and 5 : 7 respectively. These alloys are melted in the ratio 1 : 2 to form a third alloy C. The ratio of tin and copper in the alloy C is
A and B are two alloys of copper and tin prepared by mixing metals in the ratio of 4 : 3 and 5 : 7 respectively. These alloys are melted in the ratio 1 : 2 to form a third alloy C. The ratio of tin and copper in the alloy C is
1). 65 : 53
2). 67 : 59
3). 65 : 67
4). 68 : 55
1 answers
Let 1 kg of the alloy A and 2 kg of alloy B are mixed together
In 1 kg of alloy A,
Quantity of copper = $(\frac{4}{7})$ kg
Quantity of tin = $(\frac{3}{7})$ kg
In 2 kg alloy B,
Quantity of copper = $(2\; \times \;\frac{5}{{12}} = \;\frac{5}{6})$ kg
Quantity of tin = $(2\; \times \;\frac{7}{{12}} = \;\frac{7}{6})$ kg
∴ Required ratio of = $(\left( {\frac{3}{7} + \;\frac{7}{6}} \right) \sim \left( {\frac{4}{7} + \;\frac{5}{6}} \right) = \;\frac{{67}}{{42}} \sim \frac{{59}}{{42}} = \frac{{67}}{{59}})$
∴ Required ratio = 67 ? 59