Maths Olympiad - exercise your grey matter!

[Marshmallowman]

they don't say they are dry, but we know that the componet of the weight of the mushrooms with no water MUST remain constant(unless someone eats some of them)

so intially they are 1% of the total weight, but after drying they are 2 %

using your figures

9.9kg *0.98 = 9.702 kg
9.9kg *0.02 = 0.198 kg

where did the extra .098 kg of mushroom without water come from?

[Dilitante1]

they don't say they are dry, but we know that the componet of the weight of the mushrooms with no water MUST remain constant(unless someone eats some of them)

so intially they are 1% of the total weight, but after drying they are 2 %

using your figures

9.9kg *0.98 = 9.702 kg
9.9kg *0.02 = 0.198 kg

where did the extra .098 kg of mushroom without water come from?

10 Kg of shrooms at 99% water weight
now 10 Kg -1% water weight = 9.9 Kg

[Umfriend]

2. A box of fresh mushrooms weighs 10 kg. At first, water made up 99% of the weight of mushrooms.

So here we have 99% of 10 kg = 9.9 kg is water and therefore, 1% of 10 kg = 0.1 kg is, let's say, Solid Mass (SM).

After a while, the mushrooms have dried up

Can we agree that this does not affect SM? And that that therefore still is 0.1 kg?

so that now water makes up only 98% of their weight. How much does the box of mushrooms weigh now?

As water makes up 98%, SM must equal 2%. SM must also equal 0.1 kg. Divide by 2 and multiply by 100 to get 100% of the weight of Water and SM:
0.1 kg x 100 / 2 = 5.0 kg

Reality check: If total mass is 5.0 kg and SM is 0.1 kg, Water must be 4.9 kg. 4.9 kg / 5.0 kg x 100% = 98% indeed...

Uppance (I have always wanted to say that even though I do not know what it means): It does not say that 1% of the total weight has evaporated. It says that some water has evaporated such that water makes up 98% of the remaining total weight.