A and B are the two alloys of copper and brass prepared by mixing metals in the proportion of 7 : 2 and 7 : 11 respectively. If equal quantities of two alloys are melted to form a third alloy called C, then the proportion of copper and brass in C will be

Question: A and B are the two alloys of copper and brass prepared by mixing metals in the proportion of 7 : 2 and 7 : 11 respectively. If equal quantities of two alloys are melted to form a third alloy called C, then the proportion of copper and brass in C will be

Solution:
Let, A is 18 kg
copper = 18 × (7/9)
= 14 kg
brass = 4 kg

Let, B is 36 kg
copper = 36 × (7/18)
= 14 kg
brass = 22 kg

After mixing, total amount = 18 + 36 = 54 kg

From part A, copper = (54/2) × (7/9) = 21 kg
brass = 27 - 21 = 6 kg

From part B, copper = (54/2) × (7/18) = 10.5 kg
brass = 27 - 10.5 = 16.5 kg

Ratio = (21 + 10.5) : (6 + 16.5)
= 31.5 : 22.5
= 315 : 225
= 63 : 45
= 7 : 5