Multiple choice

A jar was full with honey. A person to drawn out 20% of the honey from the jar and replaced it with sugar solution. He done the same process 4 times and thus there was only 512 gm of honey left in the jar, the rest part of the jar was filled with the sugar solution. The initial amount of honey in the jar was:

  1. 1.25 kg

  2. 1 kg

  3. 1.5 kg

  4. 2.4 kg
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A Correct answer
Explanation

The formula for the remaining amount of honey is A = P(1 - r/100)^n. Here, 512 = P(1 - 20/100)^4, which is 512 = P(0.8)^4. 512 = P(0.4096), so P = 512 / 0.4096 = 1250 grams, which is 1.25 kg.

AI explanation

Using the replacement formula, the final amount of the original liquid is the initial amount multiplied by the fraction of the liquid retained, raised to the number of times the replacement occurs. Here, 20 percent is removed each time, so 80 percent, or the fraction 4/5, is retained over 4 operations. The equation is Initial Amount multiplied by (4/5)^4 equals 512 grammes, which is the same as Initial Amount multiplied by 256/625 equals 512. Solving for the initial amount gives 512 multiplied by 625 and divided by 256, yielding 1250 grammes, or 1.25 kg.

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