36 kilograms of fresh dates contain 0.1*36=3.6 kilograms of non-water.

Dry dates obtained from these fresh dates will contain the same amount of non-water and we are told that this amount should be 72% of the dry dates, thus x*0.72=3.6 --> x=5 kilograms.

Answer: A.

Similar questions to practice:
each-of-the-cucumbers-in-100-pounds-of-cucumbers-is-composed-102354.html
five-kilograms-of-oranges-contained-98-of-water-141401.html

Hope it helps.
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Given information can be rephrased as " Fresh dates contain 10% fruit while dry dates contain 72% fruit"

Hence 36 Kg of fresh dates contain 10% of 36 = 3.6 Kg of fruit.
This same amount of fruit is present after the dates are dried.
If we assume the mass of the dry dates obtained as x Kg, then 72% of x = 3.6
\(0.72*x = 3.6\)
Hence x = 5 Kg
Option A is the correct answer

I am very much interested to know how this question be done with alligation method ? I tried, but i am missing some elements.

Thanks & Regards
Vinni

Responding to a pm:

Personally, I would use the method used by Bunuel above. But if you insist on using the "alligation method" which we call "scale method", here is how you can do it:

What two things are mixed to give the third?
Dry dates are mixed with water to give fresh dates.

Dry dates have 28% water, water is 100% water and fresh dates have 90% water.

Dry dates/water = w1/w2 = (A2 - Aavg)/(Aavg - A1) = (100 - 90)/(90 - 28) = 10/62 = 5/31
Mixing 5 kg of dry dates with 31 kg (to maintain consistency) of water will give you 36 kg of fresh dates.

Answer 5 kg
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Fresh dates 36 kg = 90% water and 10% pure dates part. So pure dates part= 36 *0.1= 3.6 kg pure date.
Dry dates say x kg = 28% water and 72% pure dates part. So pure dates part= x *0.72= 0.72x kg pure date.

Equate the pure dates part only, since that quantity is same in both mixture,so 0.72 x = 3.6
x= 3.6/0.72 = 360/72 = 5 kg. Ans A

why can't i resolve this problem by putting together these 2 equations:
1 F=0.9W
2 D=0.28W

D= (0.28F)/0.9

i don't understand what is my error

Because both equations are wrong. Should be:

W=F*0.1 --> W=36*0.1=3.6 kilograms.
W=D*0.72 --> 3.6=D*0.72 --> D=5 kilograms.

For more check here: fresh-dates-contain-90-water-while-dry-dates-contain-143245.html#p1148409 and here: fresh-dates-contain-90-water-while-dry-dates-contain-143245.html#p1220200

Hope it helps.
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1. Non-water percentage of fresh grapes and dry grapes are 10% and 72% resp i.e., 7.2 times more in the dry grapes
2. So from 36 kg fresh grapes we can obtain 36/7.2 = 5 kg of dry grapes.
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Just wanted to chip in my 2 cents for the question…

Since a fresh date is 10% non-water and a dry date is 72% non-water then the ratio of non-water for the dry date to the non-water for the fresh date is 10/72 or 5/36. Meaning that for every 36 units of non-water in a fresh date there is 5 units of non-water in the dry date. Hence A

Weight of elements in 36 kg (fresh dates) water=32.4 kg, other- 3.6 kg
To make dry dates out of it some water has to be removed . Let it be x.
Weight (dry dates) water = 32.4 -x, other - 3.6 kg
Proportion of elements(dry dates) water = 28, other -72

(32.4 -x) / 3.6 = 28/72

From which we can find weight of water to be 1.4 kg and therefore total weight of dry dates = 5 kg.
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fresh date -90% water
10% no water
Dry date -28% water
72% no water
need to find weight of fry dates from 36 fresh grapes=let it be x

constant is non water portion
36 * 10%=72%x

x=5kg

Hi,

I tried solving the other way round i.e by equating % of water amount.

0.9 * 36 = 0.28 * d. This doesn't result in 5 kg weight. Why wouldn't this work? Please clarify.

You cannot equate these two because the amount of water is not equal in these two cases. You get dry dates by removing water from fresh dates.
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I have the same problem. Can't we divide the total amount of water in 36 kgs across to get the dried grapes?

dry substance in fresh date:

(10/100)*36=3.6kg

3.6kg = 72%
xkg =100%

x=(3.6*100)/72, x=5kg

A

weight * concentration = constant

w1*c1 = w2*c2

36 * 10/100 = w2 * 72/100

w2 = 5 kg.
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the weight of substance other than water is not changing. Only its concentration is changing.
(10*36)/100 = (72*X)/100
X = 5 kg
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let the weight of dry dates to be obtained be x

36 kg dates have 0.9*36 = 32.4 kg water and 3.6 kg other stuff

other stuff will also be (1-0.28)x

equating we get
(1 - 0.28)x = 3.6

or x = 3.6/0.72 = 5kg

Option A

My Take:

Generally:
(A1*W1 + A2*W2) / (W1 + W2) = Aavg

In this case:(Water evaporates)
(A1*W1 - A2*W2) / (W1 - W2) = Aavg

=> (90*36 - 100*n) / (36 - n) = 28; Here water concentration = 100% and weight of water = n
=> 90*36 - 100n = 28*36 - 28n
=> 36(90-28) = 100n - 28n
=> 36*62 = 72n
=> 2n = 62
=> n = 31
Therefore, weight of dry dates = weight of fresh dates - weight of water evaporated = 36 - 31 = 5 kgs