Multiple choice

A mixture contains two types of grains in the ratio of 7 : 12. Another mixture contains the same two types of grains in the ratio of 4 : 9. If 10 kg of the first mixture is mixed with 8 kg of the second mixture, then what will be the ratio of the two types of grains in the resultant mixture?

  1. 31 : 96

  2. 51 : 96

  3. 21 : 66

  4. 41 : 90

  5. 26 : 35
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B Correct answer
AI explanation

In the first 10 kg mixture, the two grains are (10 multiplied by 7 divided by 19) and (10 multiplied by 12 divided by 19), which equals 70 divided by 19 and 120 divided by 19. In the second 8 kg mixture, they are (8 multiplied by 4 divided by 13) and (8 multiplied by 9 divided by 13), which equals 32 divided by 13 and 72 divided by 13. Adding these respective quantities gives (910 plus 608) divided by 247 for the first grain, which is 1518 divided by 247, and (1560 plus 1368) divided by 247 for the second, which is 2928 divided by 247. The resulting ratio is 1518 to 2928, and dividing both sides by 30 simplifies this to 51 to 96.

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