Multiple choice

Two containers X and Y contain chemical and water in the ratios of 4 : 3 and 2 : 3, respectively. Find the ratio in which the two solutions from X and Y should be mixed to obtain a new solution containing half chemical and half water.

  1. X : Y = 7 : 4

  2. X : Y = 7 : 5

  3. X : Y = 5 : 4

  4. X : Y = 7 : 6

  5. X : Y = 6 : 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the method of alligation: Container X has 4/7 chemical, Container Y has 2/5 chemical, and the mixture needs 1/2 chemical. The differences are |4/7 - 1/2| = 1/14 and |2/5 - 1/2| = 1/10. The ratio is (1/10) : (1/14) = 14 : 10 = 7 : 5.

AI explanation

In container X, the ratio of chemical to water is 4 : 3, making the proportion of chemical 4/7. In container Y, the ratio of chemical to water is 2 : 3, making the proportion of chemical 2/5. The new mixture must be half chemical, meaning the target proportion is 1/2. Using the alligation method, the ratio of X to Y is (1/2 minus 2/5) : (4/7 minus 1/2), which simplifies to 1/10 : 1/14, yielding a final ratio of 7 : 5.

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