Average, Mixture and Alligation Question 4 - CAT 2021
If a certain weight of an alloy of silver and copper is mixed with 3 kg of pure silver, the resulting alloy will have 90% silver by weight. If the same weight of the initial alloy is mixed with 2 kg of another alloy which has 90% silver by weight, the resulting alloy will have 84% silver by weight. Then, the weight of the initial alloy, in kg, is:
Step-by-Step Explanation
Let the initial alloy have a total weight of W kg, and contain S kg of silver.
- Scenario 1 (Mixed with 3 kg pure silver):
The new mixture has 90% silver content:
(S + 3) / (W + 3) = 0.90 ⟹ S + 3 = 0.90W + 2.7 ⟹ S = 0.90W − 0.3 --- (Equation 1)
- Scenario 2 (Mixed with 2 kg of 90% silver alloy):
Silver added from the second alloy = 2 × 0.90 = 1.8 kg. The new consolidated mixture has 84% silver content:
(S + 1.8) / (W + 2) = 0.84 ⟹ S + 1.8 = 0.84W + 1.68 ⟹ S = 0.84W − 0.12 --- (Equation 2)
- Equate the expressions for S:
0.90W − 0.3 = 0.84W − 0.12
0.06W = 0.18 ⟹ W = 0.18 / 0.06 = 3 kg
The weight of the initial alloy is 3 kg.
Correct Option: C
💡 FundaMakers Tip:
Notice that in both scenarios, the target mix additions are related to a 90% reference baseline. Instead of setting up full fractional equations for the individual weights, you can think of this as an Alligation problem tracking the deviations from the 90% benchmark, which allows you to solve the system using simple linear scale steps.