Question

In a 2 kg mixture of copper and aluminum, 30% is copper. How much aluminum powder should be added to the mixture so that the quantity of copper becomes 20%?
A. 900 grams
B. 800 grams
C. 1000 grams
D. 1200 grams

Answer 1

Hint: First of all, find the weight of copper in the given 2 kg mixture of aluminum and copper. Then take the weight of the aluminum as a variable which is to be added to the mixture so that the quantity of the copper becomes 20%. As the weight of the copper remains as it is in the newly formed mixture, we can find out the variable which is the required answer.

Complete step-by-step answer:

The total mixture of copper and aluminum = 2 kg = 2000 grams
Given copper percent = 30%
So, weight of copper in the mixture $= \dfrac{{30}}{{100}} \times 2000 = 600{\text{ grams}}$
Let $x$ grams are added to the mixture so that the quantity of copper becomes 20%.
Now, total mixture of copper and aluminum becomes = 2000 grams + $x$ grams = (2000 + $x$) grams
And the percentage of copper becomes 20% but the weight remains as it is i.e., 600 grams.
So, 20% of (2000 + $x$) grams = 600 grams

$$\dfrac{{20}}{{100}} \times \left( {2000 + x} \right) = 600 \\\ 20\left( {2000} \right) + 20x = 600 \times 100 \\\ 40000 + 20x = 60000 \\\ 20x = 60000 - 40000 \\\ 20x = 20000 \\\ \therefore x = \dfrac{{20000}}{{20}} = 1000 \\\$$

Hence 1000 grams of aluminium should be added to the mixture so that the quantity of copper becomes 20%.
Thus, the correct option is B. 1000 grams

Note: The $x\%$ of $y$ is given by $\dfrac{x}{{100}} \times y$. Whenever a substance is added to change the percentage of another substance, the weight of that substance remains the same in the formed mixture. So, use this concept to solve these types of problems.