Question

In two alloys, copper and Zinc are related in the ratio of $ 4:1 $ and $ 1:3 $ . 10 Kg of 1st alloy, 16 kg of 2nd alloy and some of pure copper are melted together in which ratio of copper to zinc was $ 3:2 $ . find the weight of the new alloy.
A. 35 Kg
B. 45 Kg
C. 40 Kg
D. 50 Kg

Answer 1

Hint: We first assume the weight of the pure copper. Then we find the individual amount of copper and Zinc in the two alloys that are given. We have to add the individual amounts and then find the ratio of the copper and zinc.

Complete step by step solution:
Let’s assume the pure copper that has been added is of weight $ x $ kg.
In 10 Kg of 1st alloy the ratio of copper and Zinc is $ 4:1 $ .
Therefore, the exact weight of individual copper and Zinc is $ \dfrac{10\times 4}{4+1}=8 $ and $ \dfrac{10\times 1}{4+1}=2 $ .
In 16 kg of 2nd alloy the ratio of copper and Zinc is $ 1:3 $ .
Therefore, the exact weight of individual copper and Zinc is $ \dfrac{16\times 1}{3+1}=4 $ and $ \dfrac{16\times 3}{3+1}=12 $ .
The new alloy contains a total amount of copper as $ 8+4+x=x+12 $ and zinc as $ 2+12=14 $ kg.
In new alloy the ratio of copper to zinc is $ 3:2 $ .
Therefore, $ \dfrac{x+12}{14}=\dfrac{3}{2} $ . We solve the equation to get
 $
   \dfrac{x+12}{14}=\dfrac{3}{2} \\
  \Rightarrow 2x+24=42 \\
  \Rightarrow 2x=42-24=18 \\
  \Rightarrow x=\dfrac{18}{2}=9 \;
 $
So, the total weight of the new alloy is $ 10+16+9=35 $ kg. The correct option is A.
So, the correct answer is “Option A”.

Note: It’s better to assume the weight of the pure copper than assuming the total weight for the new alloy as that helps in calculation. The ratio of the items helps us find the proportional fraction value of the respective items.