Multiple choice

A bottle is full of dettol One third of it is taken out and then an equal amount of water is poured into the bottle to fill it This operation is done four times Find the final ratio of dettol and water in the bottle

  1. 13 : 55

  2. 20 : 74

  3. 16 : 65

  4. 10 : 48
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The formula for the final concentration of the original liquid after n replacements is: Final = Initial * (1 - x/y)^n. Here, 1/3 is replaced, so 2/3 remains. After 4 operations, the ratio of dettol to total volume is (2/3)^4 = 16/81. Thus, dettol is 16 parts and water is 81 - 16 = 65 parts. The ratio is 16:65.

AI explanation

When a fraction of a liquid is repeatedly replaced, the formula for the remaining original liquid is (Final Amount) = (Initial Amount) * (1 - Replaced Fraction)^n. Here, the replaced fraction is 1/3 and the operation is performed 4 times, so the remaining dettol is 1 * (1 - 1/3)^4 = (2/3)^4 = 16/81. The water fills the rest of the bottle, making its quantity 1 - 16/81 = 65/81. The final ratio of dettol to water is 16 to 65.

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