Average, Mixture and Alligation Question 4 - CAT 2020
An alloy is prepared by mixing three metals A, B and C in the proportion 3 : 4 : 7 by volume. Weights of the same volume of the metals A, B and C are in the ratio 5 : 2 : 6. In 130 kg of the alloy, the weight, in kg, of the metal C is:
Step-by-Step Explanation
The total absolute weight of a component in an alloy depends on the combined effect of its volume and its specific unit weight (density proxy).
Weight ∝ Volume × Unit Weight Ratio
- Determine the Final Weight Proportions:
Metal A: 3 × 5 = 15 parts
Metal B: 4 × 2 = 8 parts
Metal C: 7 × 6 = 42 parts
Total Proportion Sum = 15 + 8 + 42 = 65 parts
- Calculate the Absolute Weight of Metal C:
The total weight of the alloy is 130 kg.
Weight of Metal C = 42 / 65 × 130 = 42 × 2 = 84 kg
Correct Option: B
💡 FundaMakers Tip:
Whenever you encounter cross-product ratio scales (like volume ratios mixed with weight-per-volume ratios), create a compound ratio matrix by multiplying the terms directly. Notice how the total parts sum (65) divides into the total target weight (130 kg) by a clean factor of 2, making the final calculation easy.