Multiple choice

Rita blends two types of mixture to create a new mixture. She mixes apple juice with orange juice in the ratio 2 : 3 to prepare mixture X, and pineapple juice with orange juice in the ratio 3 : 4 to prepare mixture Y. She then combines mixtures X and Y in the ratio 5 : 7 to create a new mixture Z. If she dilutes mixture Z with an equal amount of water to make a refreshing beverage, what percentage of the refreshing beverage is orange juice?

  1. 12.5%

  2. 25%

  3. 29.17%

  4. 58.33%

  5. na
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Mixture X has orange juice in ratio 3/5. Mixture Y has orange juice in ratio 4/7. Combining X and Y in 5:7 ratio: Total orange = (5 * 3/5 + 7 * 4/7) / (5 + 7) = (3 + 4) / 12 = 7/12. Diluting with equal water means the new total volume is doubled, so orange juice percentage is (7/12) / 2 = 7/24, which is approximately 29.17%.

AI explanation

Take 60 units of mixture X, containing 24 units of apple juice and 36 units of orange juice, and 70 units of mixture Y, containing 30 units of pineapple juice and 40 units of orange juice. Mixing these gives 130 units of mixture Z containing 76 units of orange juice. When diluted with an equal amount of 130 units of water, the total volume becomes 260 units, making the percentage of orange juice (76 / 260) * 100, which is 29.17 percent.

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