Percentages Question 3 - CAT 2021
If a certain weight of an alloy of silver and copper is mixed with 3 kg of pure silver, the resulting alloy contains 90% silver by weight.
If the same quantity of the original alloy is mixed with 2 kg of another alloy containing 90% silver, the resulting alloy contains 84% silver by weight.
The weight of the original alloy, in kilograms, is:
Step-by-Step Explanation
Let the original alloy contain:
- x kg of silver
- y kg of copper
Using the first condition,
(x + 3) / (x + y + 3) = 90 / 100
which simplifies to
9y − x = 3
Using the second condition,
(x + 1.8) / (x + y + 2) = 84 / 100
which simplifies to
21y − 4x = 3
Solving these two equations,
x = 2.4, y = 0.6
Therefore,
x + y = 3 kg
Hence, the correct answer is Option C.
💡 FundaMakers Tip: In alloy questions, write equations based on the amount of the metal, not the percentage.