Multiple choice

Tin and Cobalt are mixed in the respective ratio of 1 : 2 to form an alloy 1. Later, they are mixed in the ratio of 2 : 3 to form alloy 2. Then, these two alloys are mixed to form another alloy in which tin to cobalt ratio is 5 : 8. What is the ratio of alloy 1 to alloy 2 in the newly formed alloy?

  1. 3 : 10

  2. 3 : 7

  3. 10 : 3

  4. 7 : 3

  5. 4 : 7
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A Correct answer
Explanation

Using the alligation method: Alloy 1 has 1/3 tin, Alloy 2 has 2/5 tin, and the mixture has 5/13 tin. The differences are |2/5 - 5/13| = 1/65 and |1/3 - 5/13| = 2/39. The ratio is (1/65) / (2/39) = (1/65) * (39/2) = 39/130 = 3/10.

AI explanation

By the rule of alligation applied to the proportion of Tin in the alloys, Alloy 1 has 1/3 Tin and Alloy 2 has 2/5 Tin. The final mixture has 5/13 Tin. The ratio of Alloy 1 to Alloy 2 is therefore (5/13 minus 2/5) divided by (1/3 minus 5/13). This equals (-1/65) divided by (-2/39), which results in a ratio of 3 to 10. The ratio of Alloy 1 to Alloy 2 in the new alloy is 3 : 10.

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