Multiple choice

A mixture is made of two kinds of chemicals. The chemicals are in the ratio 3 : 2. Another mixture is made of the same two chemicals, but in this, the chemicals are in the ratio 4 : 5. How much quantity of the other mixture must be mixed with 3 L of the former mixture so that the resulting mixture may contain equal quantities of both the chemicals?

  1. 5 2 5 L

  2. 5 2 3 L

  3. 4 1 2 L

  4. 3 3 4 L

  5. 2 1 3 L
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In 3 L of the first mixture, the quantities are 1.8 L and 1.2 L. If x litres of the second mixture are added, its quantities are 4x/9 and 5x/9; equating the final quantities gives x = 5.4 L, or 5 2/5 L.

AI explanation

In the first mixture, the proportion of chemical one is 3/5, and in the second mixture, it is 4/9. The required proportion in the final mixture is 1/2 since both chemicals must be equal. Applying the rule of alligation, the ratio of the quantities to be mixed is (1/2 - 4/9) to (3/5 - 1/2), which simplifies to 1/18 and 1/10. This gives a mixture ratio of 5 to 9. If 5 parts equal 3 L, then 9 parts equal 27/5 L, which is 5 2/5 L.

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