Multiple choice

Two mixtures A and B are in the ratio 5 : 4, respectively. Mixture A contains p% of paint and q% of thinner, and mixture B contains r% of paint and s% of thinner. If mixture A is mixed with mixture B, the final quantity of paint becomes 30% of the total volume of final mixture. If p - r = 27, find p : r.

  1. 5 : 14

  2. 14 : 5

  3. 15 : 4

  4. 4 : 15

  5. 16 : 5
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B Correct answer
Explanation

Let volumes be 5x and 4x. Total volume = 9x. Paint = (p/100)*5x + (r/100)*4x = 0.30 * 9x. 5p + 4r = 270. Given p - r = 27 => p = r + 27. Substitute: 5(r+27) + 4r = 270 => 9r + 135 = 270 => 9r = 135 => r = 15. Then p = 42. p:r = 42:15 = 14:5.

AI explanation

By the rule of alligation, the ratio of the quantities of mixture A to mixture B equals (30 minus r) divided by (p minus 30), which is given as 5 to 4. This means 120 minus 4r equals 5p minus 150, and using the given p minus r equals 27 to substitute r with p minus 27 results in 120 minus 4p plus 108 equaling 5p minus 150. Solving this equation gives p as 42 and r as 15, making their ratio 14 to 5.

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