Multiple choice

In two types of stainless steels, the ratios of chromium to steel are 2 : 11 and 5 : 21. In what proportion should the two types be mixed so that the ratio of chromium to steel in the new type becomes 7 : 32?

  1. 2 : 3

  2. 3 : 4

  3. 1 : 2

  4. 1 : 3
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C Correct answer
Explanation

Use alligation on the chromium fraction. Type 1: 2/13. Type 2: 5/26. Target: 7/39. (7/39 - 5/26) / (2/13 - 7/39) = ((14-15)/78) / ((6-7)/39) = (-1/78) / (-1/39) = 39/78 = 1/2.

AI explanation

Convert the given ratios into fractions of chromium: the first type is 2/13 and the second type is 5/26, while the desired mixture must be 7/39. Using the method of alligation, calculate the differences to find the ratio: (5/26 - 7/39) : (7/39 - 2/13), which simplifies to (15 - 14)/78 : (14 - 12)/78. This results in a ratio of 1 : 2 for mixing the two types.

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