Question

Alloy contains copper and zinc in the ratio of 5:3 and another contains copper and tin in the ratio of 8:5. If equal weights of the two are melted together to form a new alloy, find the weight of tin per kg in the new alloy.

Answer 1

8+5=13
Assume 13 kg of both the alloys are melted together.

Weight of tin in the resulting alloy =13×5/13=5 kg
Total weight of the resulting alloy =13+13=26 kg

i.e., in 26 kg of the resulting alloy, weight of tin is 5 kg.

Therefore, weight of tin in the resulting alloy per kg
=5/26 kg

Answer 2

Solution:

Let us assume the weight of both alloys A and B, be 1 kg each.

Ratio of copper and tin in alloy B = 8:5

$\Rightarrow 8x+5x = 1\\\Rightarrow 13x = 1\\\Rightarrow x =\frac{1}{13}$

Weight of tin in alloy B = $5x$ g

Weight of tin in alloy B =   $5 \times \frac{1}{13}$ kg

Weight of tin in alloy B = $\frac{5}{13}$ kg

Weight of tin in alloy A = 0 kg

Because in alloy A, only Copper and Zinc are present.

When both alloy are melted together, then weight of new alloy = 2 kg

Weight of tin in 2 kg of new alloy = $\frac{5}{13}$ kg

Weight of tin per kg in the new alloy = $\frac{1}{2} \times \frac{5}{13}$ kg

Weight of tin per kg in the new alloy = $\frac{5}{26}$ kg