There are two bars made of gold-silver alloy. The first bar contains $2$ parts of gold and $3$ parts of silver by weight, while the second contains $3$ parts of gold and $7$ parts of silver by weight. If both bars are melted and combined to form a single $8$-kilogram bar with a gold-to-silver ratio of $5:11$ by weight, what was the weight of the first bar?

Classic alligation setup. The first bar is 40% gold and the second is 30% gold, and the target is 5/16 = 31.25%. Since gold fractions are close, the two weights should be very lopsided toward the second bar. That immediately kills C, D, E for me.

I set up x + y = 8 and then (2/5)x + (3/10)y = (5/16)(8). Solving gave a clean number. Took me about 90 seconds, feels right for 700 level.

Is anyone else getting tripped up by the wording? It says 2 parts gold and 3 parts silver, so the gold fraction is 2/5, not 2/3. I wasted a minute because I misread it the first time.

Alligation shortcut: gold fractions 2/5=40%, 3/10=30%, mixture 5/16=31.25%. Differences are 8.75 and 1.25, so the ratio of weights is 1.25:8.75 = 1:7. Since total is 8 kg, the first bar is the smaller share.