Question

In what proportion should two types of gold-one of 24 carats and another of 16 carats purity, be mixed to get gold of 18 carats purity?

Answer 1

Answer:  The required proportion is 1 : 3.

Step-by-step explanation:  We are given to find the proportion in which two types of gold-one of 24 carats and another of 16 carats purity should be mixed to get gold of 18 carats purity.

Let the required proportion be x : y.

Then, according to the given information, we have

$\dfrac{24\times x+16\times y}{x+y}=18\\\\\Rightarrow 24x+16y=18(x+y)\\\\\Rightarrow 24x+16y=18x+18y\\\\\Rightarrow 24x-18x=18y-16y\\\\\Rightarrow 6x=2y\\\\\Rightarrow 3x=y\\\\\Rightarrow \dfrac{x}{y}=\dfrac{1}{3}\\\\\Rightarrow x:y=1:3.$

Thus, the required proportion is 1 : 3.