A 5 kg watermelon contains 99% water by weight. Some of the water evaporates and the melon now contains 98% water by weight. What is the weight (in kg) of watermelon now?
Part ACSIR NET September 2022track-the-invariant-part
Track the invariant part
- A.4.5
- B.2.5✓
- C.4.8
- D.4.9
The idea, in plain words
The water evaporates but the solid pulp does not, so follow the pulp instead. It begins as one percent of the melon and ends as two percent, so the melon must have halved — even though the water figure barely moved.
Solution
The solid matter is 1% of 5 kg = 0.05 kg and does not evaporate. Afterwards it is 2% of the new weight W, so 0.05 = 0.02 W and W = 2.5 kg. Tracking the part that stays constant, rather than the water, is what makes this tractable.
Why each option is right or wrong
Checked against 1 symbolic computation- A.WrongExecution slip
False, and 4.5 is what intuition suggests: the water fraction fell by only one percentage point, so surely the melon barely changed. It did not — the solid matter went from 1% to 2% of the total, which means the total had to halve.
- B.Correct
True. Track the solid, which does not evaporate: it is 1% of 5 kg = 0.05 kg throughout. Afterwards the solid is 2% of the new weight W, so 0.05 = 0.02 W and W = 2.5 kg (verified). The trigger: in any evaporation or concentration problem, follow the quantity that stays fixed — here doubling the solid's share from 1% to 2% forces the total to halve.
- C.WrongExecution slip
False. 4.8 comes from subtracting a small amount of water proportional to the one-point change, treating percentages as if they subtract directly. The relevant ratio is between the solid fractions, 1% and 2%, which differ by a factor of two rather than by one point.
- D.WrongExecution slip
False. 4.9 is 5 minus 1% of 5, that is removing 0.05 kg — the weight of the solid rather than the weight of the evaporated water. The water lost is 4.95 − 2.45 = 2.5 kg, fifty times larger.
3 of these 3 wrong options correspond to a named reasoning error — the same errors recur across subjects.