Multiple choice

A drum contains 20 litres of a paint. From this 2 litres of paint is taken out and replaced by 2 litres of oil. Again 2 litres of this mixture is taken out and replaced by 2 litres of oil. If this operation is performed once again, then what would be the final ratio of paint and oil in the drum ?

  1. $\displaystyle \frac{719}{371}$
  2. $\displaystyle \frac{709}{291}$
  3. $\displaystyle \frac{727}{273}$
  4. $\displaystyle \frac{729}{271}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial paint = 20. After 3 replacements of 2L: Final paint = 20 * (1 - 2/20)^3 = 20 * (0.9)^3 = 20 * 0.729 = 14.58. Oil = 20 - 14.58 = 5.42. Ratio Paint/Oil = 14.58 / 5.42 = 1458 / 542 = 729 / 271.

AI explanation

Using the formula for repeated replacement, the remaining amount of paint is 20 * (1 - 2/20)^3 = 20 * (9/10)^3 = 20 * 729/1000 = 14.58 L. Because the drum's total capacity remains 20 L, the final amount of oil is 20 - 14.58 = 5.42 L. The resulting ratio of paint to oil is 14.58 to 5.42, which equals 1458 to 542 or 729 to 271.

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