Multiple choice

For making a colour A, three liquids x, y and z are mixed in the ratio 3 : 5 : 7. For colour B, the ratio is 1 : 8 : 3. If 10 parts of colour A are mixed with 8 parts of colour B, what is the ratio of liquids x, y and z in the resulting mixture?

  1. 11 : 25 : 17

  2. 31 : 27 : 30

  3. 18 : 25 : 19

  4. 4 : 13 : 10

  5. None of these
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D Correct answer
Explanation

A: x=3/15, y=5/15, z=7/15. B: x=1/12, y=8/12, z=3/12. 10 parts A + 8 parts B: x = 10*(3/15) + 8*(1/12) = 2 + 2/3 = 8/3. y = 10*(5/15) + 8*(8/12) = 10/3 + 16/3 = 26/3. z = 10*(7/15) + 8*(3/12) = 14/3 + 2 = 20/3. Ratio = 8:26:20 = 4:13:10.

AI explanation

To find the parts of x, y, and z in the resulting mixture, calculate the weighted sum from both colours: for 10 parts of colour A, multiply the ratio components by 10 divided by 15, yielding 2, 3.33, and 4.67 parts respectively. For 8 parts of colour B, multiply the components by 8 divided by 12, yielding 0.67, 5.33, and 2 parts. Adding these provides total parts of x equal to 2.67, y equal to 8.66, and z equal to 6.67, which simplifies by dividing by 0.67 to give the final ratio of 4 to 13 to 10.

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