Question

An alloy of copper and zinc is taken in the ratio $1:2$, and another alloy of the same metal is takn in the ratio of $2:3$. How many parts of the alloys must be taken to obtain a new alloy consisting of copper and zinc that are taken in the ratio $3:10$?

• A. $7$ and $9$
• B. $5$ and $8$
• C. $3$ and $5$
• D. $5$ and $3$

Answer 1

Answer: (B)

$5$ and $8$

Let them be mixed in the ratio x : y

Then, in $1_{st}$ alloy, Zinc = $\frac{x}{3}$

and Copper = $\frac{2x}{3}$

$2_{nd}$ alloy, Zinc = $\frac{2y}{5}$

and Copper = $\frac{3y}{5}$

Now, we have

$\frac{x}{3}+\frac{2y}{5}:\frac{2x}{3}+\frac{3y}{5}=5:8$

$⟹\frac{5x+6y}{10x+9y}=\frac{5}{8}$

$⟹40x+48y=50x+45y$

$⟹10x=3y$

$\therefore \frac{x}{y}=\frac{3}{10}$

Thus, the required ratio = $3:10$.