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

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Option C. 5/26

Let 104 kg of each be melted.

then copper in the first alloy = 104×5/8 = 65 kg.

Zinc in the first alloy = 104×3/8 = 39 kg.

Copper in 2nd alloy = 104×8/13 = 64 kg

Tin in 2nd alloy = 104×5/13 = 40 kg.

Total alloy = 104 + 104 = 208 kg.

Weight of tin per kg. = $\frac{40}{208}$ = $\frac{5}{26}$.