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 are5:3and1:2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio4:3. What is the ratio of the composition of the two basic elements in alloy X?

• A. 1:1
• B. 1:3
• C. 1:4
• D. none

Answer 1

The correct option is A

1:1

The new alloy X is formed from the two alloys A and B in the ratio4:3.

Hence, 7 parts of the alloy contains 4 parts of alloy A and 3 parts of alloy B.

Let 7x ounces of alloy X contain 4x ounces of alloy A and 3x ounces of alloy B.

Now, alloy A is formed of the two basic elements mentioned in the ratio5:3.

Hence, 4x ounces of alloy A contains$\left(\frac{5}{5+3}\right)4x=\frac{5x}{2}$ounces of first basic element

And $\left(\frac{3}{5+3}\right)4x=\frac{3x}{2}$ounces of the second basic element. Also, alloy B is formed of the two basic elements mentioned in the ratio1:2.

Hence, let the 3x ounces of alloy A contain$\left(\frac{1}{1+2}\right)3x=x$ ounces of the first basic element and $\left(\frac{2}{1+2}\right)3x=2x$ounces of the second basic element.

Then the total compositions of the two basic elements in the 7x ounces of alloy X would contain$\frac{5x}{2}$ounces (from A) + x ounces (from B)=$\frac{7x}{2}$ ounces of first basic element, and$\frac{3}{2x}$ (from A) + 2x(from B)=$\frac{7x}{2}$ounces of the second basic element.

Hence, the composition of the two basic elements in alloy X is 1:1