Multiple choice

There are two drums, each containing a mixture of paints A and B. In drum 1, A and B are in the ratio 18 : 7. The mixtures from drums 1 and 2 are mixed in the ratio 3 : 4 and in this final mixture, A and B are in the ratio 13 : 7. In drum 2, A and B are in the ratio

  1. 220 : 149

  2. 229 : 141

  3. 239 : 161

  4. 251 : 163
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let drum 1 ratio be 18:7 (total 25) and drum 2 be x:y (total x+y). Mixture ratio 3:4. (3/7 * 18/25 + 4/7 * x/(x+y)) / (3/7 * 7/25 + 4/7 * y/(x+y)) = 13/7. Solving this leads to the ratio 239:161.

AI explanation

In drum 1, the fraction of paint A is 18 divided by 25, and in the final mixture, the fraction of paint A is 13 divided by 20. Since drum 1 and drum 2 are mixed in a 3 to 4 ratio, the final mixture is composed of three-seventths drum 1 and four-sevenths drum 2. Using the weighted average formula, we set up the equation three divided by 7 times 18 divided by 25 plus four divided by 7 times the drum 2 fraction equals 13 divided by 20. Solving this gives the drum 2 fraction as 239 divided by 400. This means the fraction of paint B in drum 2 is 161 divided by 400, making the required ratio 239 to 161.

Keep practicing — related questions