Multiple choice

A test tube contains 80 ml of boric acid. In an experiment, 16 ml of boric acid is removed from test tube and similar amount of glucose solution is poured in it. Again, same amount of mixture of boric acid and glucose solution is taken out of the test tube and replaced by the same amount of glucose solution. Calculate the ratio of the remaining boric acid with quantity of boric acid initially present in the test tube.

  1. 8 : 5

  2. 16 : 25

  3. 8 : 11

  4. 12 : 5

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial acid = 80. After 1st replacement: 80 * (1 - 16/80) = 80 * 0.8 = 64. After 2nd replacement: 64 * 0.8 = 51.2. Ratio of remaining acid to initial = 51.2 / 80 = 512 / 800 = 64 / 100 = 16 / 25.

AI explanation

Using the replacement formula for mixtures, the remaining quantity of boric acid is calculated as 80 multiplied by (1 minus 16 divided by 80) raised to the power of 2. This gives 80 multiplied by 0.8 squared, which equals 80 multiplied by 0.64, resulting in 51.2 ml. The required ratio of remaining boric acid to the initial quantity is 51.2 divided by 80, which simplifies to 16 : 25.

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