Multiple choice

25 kg of alloy X is mixed with 125 kg of alloy Y. If the amount of lead and tin in the alloy X is in the ratio 1 : 2 and the amount of lead and tin in the alloy Y is in the ratio 2 : 3, then what is the ratio of lead to tin in the mixture?

  1. 1 : 2

  2. 2 : 3

  3. 3 : 5

  4. 7 : 11
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D Correct answer
Explanation

Alloy X: 25 kg, 1:2 ratio (8.33 kg lead, 16.67 kg tin). Alloy Y: 125 kg, 2:3 ratio (50 kg lead, 75 kg tin). Total lead = 58.33 kg, Total tin = 91.67 kg. Ratio = 58.33/91.67 = 7/11.

AI explanation

In alloy X, the 25 kg mass contains lead and tin in a 1 to 2 ratio, meaning there is 25 divided by 3 kg of lead and 50 divided by 3 kg of tin. In alloy Y, the 125 kg mass has a 2 to 3 ratio, meaning it contains 50 kg of lead and 75 kg of tin. Adding these together, the total lead is 25 divided by 3 plus 50 kg, which equals 175 divided by 3 kg, and the total tin is 50 divided by 3 plus 75 kg, which equals 275 divided by 3 kg; the resulting ratio of lead to tin is 175 to 275, which simplifies to 7 to 11.

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