60 kg of an alloy A is mixed with 80 kg of alloy B to get a new alloy. If alloy A has zinc and copper in the ratio 7 : 5 and alloy B has zinc and copper in the ratio 3 : 7, then what is the weight of zinc in the new alloy?
59 kg
Calculating Zinc Weight in Alloy Mixture
This problem involves mixing two different alloys, each with a specific ratio of zinc and copper. We need to find the total weight of zinc in the final mixture.
Let's break down the components of each alloy:
Alloy A Composition
- Weight of Alloy A = 60 kg
- Ratio of Zinc to Copper in Alloy A = 7 : 5
The total parts in the ratio for Alloy A are \(7 + 5 = 12\). To find the weight of zinc in Alloy A, we use the ratio:
\( \text{Weight of Zinc in Alloy A} = \left(\frac{\text{Zinc part}}{\text{Total parts}}\right) \times \text{Total weight of Alloy A} \)
\( \text{Weight of Zinc in Alloy A} = \left(\frac{7}{12}\right) \times 60 \text{ kg} \)
Calculating the weight of zinc in Alloy A:
\( \text{Weight of Zinc in Alloy A} = 7 \times \left(\frac{60}{12}\right) \text{ kg} \)
\( \text{Weight of Zinc in Alloy A} = 7 \times 5 \text{ kg} \)
\( \text{Weight of Zinc in Alloy A} = 35 \text{ kg} \)
Alloy B Composition
- Weight of Alloy B = 80 kg
- Ratio of Zinc to Copper in Alloy B = 3 : 7
The total parts in the ratio for Alloy B are \(3 + 7 = 10\). To find the weight of zinc in Alloy B, we use the ratio:
\( \text{Weight of Zinc in Alloy B} = \left(\frac{\text{Zinc part}}{\text{Total parts}}\right) \times \text{Total weight of Alloy B} \)
\( \text{Weight of Zinc in Alloy B} = \left(\frac{3}{10}\right) \times 80 \text{ kg} \)
Calculating the weight of zinc in Alloy B:
\( \text{Weight of Zinc in Alloy B} = 3 \times \left(\frac{80}{10}\right) \text{ kg} \)
\( \text{Weight of Zinc in Alloy B} = 3 \times 8 \text{ kg} \)
\( \text{Weight of Zinc in Alloy B} = 24 \text{ kg} \)
Total Zinc in the New Alloy
The new alloy is formed by mixing Alloy A and Alloy B. The total weight of zinc in the new alloy is the sum of the zinc weights from Alloy A and Alloy B.
\( \text{Total weight of Zinc} = \text{Weight of Zinc in Alloy A} + \text{Weight of Zinc in Alloy B} \)
\( \text{Total weight of Zinc} = 35 \text{ kg} + 24 \text{ kg} \)
\( \text{Total weight of Zinc} = 59 \text{ kg} \)
Therefore, the weight of zinc in the new alloy is 59 kg.
Important Questions from Mixture Problems
If the ratio of alcohol and water in a mixture of 85 litres is 11 ∶ 6. How much water should be added to make the ratio 5 ∶ 3?
Two bottles A and B contain diluted acid. In bottle A, the amount of water is double the amount of acid while in bottle B, the amount of acid is 3 times that of water. How much mixture(in litres) should be taken from each bottle A and B respectively in order to prepare 5 liters diluted acid containing an equal amount of acid and water?
A solution of milk and water contains milk and water in the ratio of 3 : 2. Another solution of milk and water contains milk and water in the ratio of 2 : 1. Forty litres of the first solution is mixed with 30 litre of the second solution. The ratio of milk and water in the resultant solution is:
A 70 litre mixture has liquids A and B in the ratio 5 ∶ 9. How many litres of liquid A must be added so that the ratio becomes 2 ∶ 3?
In a mixture of 60 litres, the ratio of milk and water is 2 : 1 respectively. How much more water must be added to make its ratio 1 : 2 respectively?
