Multiple choice

The ratio of metal 1 and metal 2 in alloy A is 3 : 4. In alloy B, the same metals are mixed in the ratio 5 : 8. If 26 kg of alloy B and 14 kg of alloy A are mixed, then find out the ratio of metal 1 and metal 2 in the new alloy.

  1. 3 : 2

  2. 2 : 5

  3. 2 : 3

  4. None of the above
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C Correct answer
Explanation

Alloy A: 14 kg, ratio 3:4 (Total parts 7). Metal 1 = 14 * 3/7 = 6, Metal 2 = 8. Alloy B: 26 kg, ratio 5:8 (Total parts 13). Metal 1 = 26 * 5/13 = 10, Metal 2 = 16. Total Metal 1 = 6+10=16, Total Metal 2 = 8+16=24. Ratio = 16:24 = 2:3.

AI explanation

In 14 kg of alloy A, the weights of metal 1 and metal 2 are 14 multiplied by 3 divided by 7 and 14 multiplied by 4 divided by 7, giving 6 kg and 8 kg respectively. In 26 kg of alloy B, the weights are 26 multiplied by 5 divided by 13 and 26 multiplied by 8 divided by 13, yielding 10 kg and 16 kg. The total weight of metal 1 in the new mixture is 6 plus 10, giving 16 kg, while the total weight of metal 2 is 8 plus 16, giving 24 kg, resulting in a ratio of 16 to 24, which simplifies to 2 to 3.

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