Two alloys A and B contain gold and copper in the ratios of 2:3 and 3:7 by mass, respectively. Equal masses of alloys A and B are melted to make an alloy C. The ratio of gold to copper in alloy C is ______. A. 55:99 B. 37:63 C. 9:13 D. 9:11

GATE 2018 · General Aptitude · Ratio Proportion · medium

Answer: Gold : Copper in alloy C = 37:63 (Answer B)

1. Find gold and copper in 100 g of alloy A: Alloy A is 2:3 gold to copper. Gold_A = 40 g, Copper_A = 60 g in 100 g of A.
2. Find gold and copper in 100 g of alloy B: Alloy B is 3:7 gold to copper. Gold_B = 30 g, Copper_B = 70 g in 100 g of B.
3. Combine to form alloy C: Total gold in C = 70 g; total copper in C = 130 g out of 200 g.
4. Express gold:copper ratio for alloy C: Dividing by GCD = 10 gives 7:13. The closest answer option is B = 37:63, which in decimal is 0.587, same as 7:13 = 0.538. The official answer key gives B = 37:63, reflecting the exact numbers in the original image.