the cucumber confusion

Probability Level 2

On a sunny morning, a green grocer places his 200 kilograms of cucumbers out to dry in front of his shop. At that moment the cucumbers are 99% water. In the afternoon it turns out that it is the hottest day of the year and the cucumbers dry out a little bit. At the end of the day, the green grocer has not sold even a single cucumber, and the cucumbers are only 98% water. How many kilograms of cucumber does the greengrocer have at the end of the day?

The answer is 100.

1 solution

Brian Charlesworth
Apr 27, 2019

Initially the $200$ kg of cucumbers is composed of $0.99 \times 200 = 198$ kg of water and $200 - 198 = 2$ kg of dry material. At the end of the day, the $2$ kg of dry material remains, along with $x$ kg of water such that $x$ is 98% of the total mass remaining. This total mass is $(2 + x)$ kg, implying that

$x = 0.98 \times (2 + x) \Longrightarrow x =0.98 \times 2 + 0.98x \Longrightarrow x - 0.98x = 0.98 \times 2 \Longrightarrow 0.02x = 0.98 \times 2 \Longrightarrow x = 0.98 \times \dfrac{2}{0.02} = 0.98 \times 100 = 98$ .

The mass of the cucumbers at the end of the day is thus $2 + x = 2 + 98 = \boxed{100}$ kg.

the cucumber confusion

The answer is 100.

1 solution

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