Question

Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are $5:3$ and $1:2$ respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio of $4:3.$ What is the ratio of the composition of the basic elements in alloy X?

• A. $1:1$
• B. $2:3$
• C. $5:2$
• D. $4:3$

Answer 1

The correct option is A $1:1$

Proportion of two basic elements in alloy A = $5:3$

Amount of first element = $\frac{5}{5+3}=\frac{5}{8}$

Amount of second element = $\frac{3}{5+3}=\frac{3}{8}$

Proportion of two basic elements in alloy B = $1:2$

Amount of first element = $\frac{1}{1+2}=\frac{1}{3}$

Amount of second element = $\frac{2}{1+2}=\frac{2}{3}$

Proportion of two alloys A and B in new alloy X = $4:3$

Let the actual amount of alloy A be $4y$ and alloy B be $3y$

$\therefore$ amount of first basic element in new alloy X

$=\frac{5}{8}\times 4y+\frac{1}{3}\times 3y=\frac{7y}{2}$

$\therefore$ Amount of second basic element in new alloy X

$=\frac{3}{8}\times 4y+\frac{2}{3}\times 3y=\frac{7y}{2}$

So, the ratio of first basic element to second in new alloy X is,

$\frac{7y}{2}:\frac{7y}{2}=1:1$

Answer is option A