Multiple choice

In a chemistry lab, there are two beakers, A and B, each containing a unique chemical solution. Beaker A holds a solution where chemicals X and Y are mixed in the ratio of 3 : 2, while beaker B contains a solution where chemicals X and Y are mixed in the ratio of 4 : 3. The chemist wants to create a new solution by combining these two solutions in a specific ratio. Find the ratio in which the solutions from beakers A and B should be mixed to create a new solution containing chemicals X and Y in the ratio of 7 : 5.

  1. 7 : 5

  2. 5 : 7

  3. 2 : 7

  4. 7 : 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Beaker A: 3/5 X, 2/5 Y. Beaker B: 4/7 X, 3/7 Y. Target: 7/12 X, 5/12 Y. Using alligation on X: |4/7 - 7/12| : |7/12 - 3/5| = |48/84 - 49/84| : |35/60 - 36/60| = 1/84 : 1/60 = 60:84 = 5:7.

AI explanation

Using the rule of alligation on the fractions of chemical X in each beaker, we compare 3/5 from beaker A and 4/7 from beaker B against the desired 7/12. The ratio of beaker A to beaker B is the difference between 4/7 and 7/12 versus the difference between 7/12 and 3/5. Calculating these differences gives 1/84 and 1/60, which simplifies to a 5 to 7 ratio when finding a common denominator.

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