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Ok, so my friends and I had a disagreement over this seemingly simple problem and we would very much like to know the answer for it.

Question

Initially a 100 kgs watermelon is 96pc water and 4pc pulp. After keeping it out in the sun for (say X) hours, the watermelon is now 95pc water. What is the weight of the watermelon now?

Answer 1

The mass of watermelon pulp initially was 4kgs. So equating that to 5pc of the current distribution would be 5/100*weight = 4kgs => X = 80Kgs

Answer 2

Assume it's a 100kg watermelon. Answer 1 is wrong as only 95pc of the 96pc water is now available. You've lost 5pc water of 96pc = 5/100* (96pc *100) = 4.8kg water. So water's total weight now is 96 - 4.8 = 91.2 kg + 4kg pulp = 95.2kgs

Can someone please explain? Thanks!

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  • $\begingroup$ Sorry to all. The orig weight of the watermelon was 100kg. Thanks for the edit. $\endgroup$ – user42479 Oct 15 '14 at 4:02
  • $\begingroup$ Answer two seems to make no sense... where does the notion come from that you have lost 5% of the 96% water? It is not in the question, and there is no piece of information that justifies that idea. $\endgroup$ – oerkelens Oct 15 '14 at 6:51
  • $\begingroup$ 91.2 is 95.798% of 95.2, so, not 95%, answer 2 is wrong. $\endgroup$ – njzk2 Oct 20 '14 at 21:13
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Ok first you need to clarify if the original weight is 20 kgs or 100kgs, assuming 100.

It was 96% water and 4% pulp i.e. 96kg and 4kg, after keeping in sun, assuming only water evaporates, its 95% water and 5% pulp.

Calculating by pulp, 5% is 4Kg so 100% is 80Kgs

Calculating by water, 95% is 95/100* 80 = 76 kgs, coming to what percentage of water was lost you cannot calculate that at all using the two numbers 96 and 95 as they are percentages of different weights.

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Originally the 20 kg watermelon consisted 19.2 kg of water (20*96%/100%) and 0.8 kg of solids (20kg*4%/100%). Assuming only water can evaporate from the melon, the solids still weigh 0.8 kg. If they make up 5% of the melon then the total weight must be w=(100%/5%)*0.8kg = 16 kg, so both your answers are wrong.

If you began with 100 kg of melon then answer 1 would be correct.

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    $\begingroup$ Dang, 8 seconds after skv... $\endgroup$ – Penguino Oct 15 '14 at 4:02
  • $\begingroup$ My question is why is Answer 2 wrong? $\endgroup$ – user42479 Oct 15 '14 at 4:03
  • $\begingroup$ Because the way you calculate differences between weights using percentage figures (of different numbers) is flawed $\endgroup$ – skv Oct 15 '14 at 4:04

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