Two alloys A and B are composed of two basic elements. The ratios of the…
2023
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 4:3. What is the ratio of the composition of the two basic elements in alloy X?
- A.
1:1
- B.
2:3
- C.
5:2
- D.
4:3
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Correct answer: A
Solution:
Step 1: Convert each alloy ratio to fractions of the two elements.
Alloy A (5:3): element1 = 5/(5+3) = 5/8, element2 = 3/8.
Alloy B (1:2): element1 = 1/(1+2) = 1/3, element2 = 2/3.
Step 2: Multiply these fractions by the amounts mixed (4 parts of A and 3 parts of B) to get total amounts.
Total of element1 = 4 * (5/8) + 3 * (1/3) = 2.5 + 1 = 3.5.
Total of element2 = 4 * (3/8) + 3 * (2/3) = 1.5 + 2 = 3.5.
Step 3: Form the final ratio of element1 to element2.
Final ratio = 3.5 : 3.5 = 1 : 1.