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# A beaker was filled with a mixture of 40 liters of water and a liquid

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
A beaker was filled with a mixture of 40 liters of water and a liquid  [#permalink]

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25 Sep 2018, 05:00
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Difficulty:

75% (hard)

Question Stats:

63% (03:07) correct 38% (03:11) wrong based on 91 sessions

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A beaker was filled with a mixture of 40 liters of water and a liquid chemical. They are fixed in the ratio of 3 : 5, respectively. If 2 percent of the initial quantity of water and 5 percent of the initial quantity of liquid chemical evaporated each day during a 10-day period, what percent of the original amount of mixture evaporated during this period?

(A) 22.22%
(B) 33.33%
(C) 38.75%
(D) 44.44%
(E) 58.33%

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Re: A beaker was filled with a mixture of 40 liters of water and a liquid  [#permalink]

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27 Sep 2018, 09:29
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A beaker was filled with a mixture of 40 liters of water and a liquid  [#permalink]

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27 Sep 2018, 10:07
780gmatpossible wrote:

780gmatpossible

so we have 40 litres of mixture (water+chemichal) in the ratio 3:5 ,

hence 3x+5x = 40 --- > 8x=40 ---> x =5

plug in this value into equation 3 (5)+5(5) = 40

water is 15 litres

chemical is 25 litres

We are told that 0.02 % of water is evaporated within ten 10 days and 0.05% of chemical is evaporated withn 10 days

0.02*10 days = 0.20 WATER
AND
0.05 *10 = 0.5 CHEMICHAL

0.20 *15 = 3 (total amount of water evaporated for 10 days )

0.50*25 = 12.5 (total amount of chemical evaporated for 10 days) ( to make it simple I will round 12.5 to 12 in final calculation below to find total mixture evaporated)

total percentage of mixture evaporated $$\frac{(3+12)}{40}= 36%$$

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Re: A beaker was filled with a mixture of 40 liters of water and a liquid  [#permalink]

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02 Oct 2018, 19:50
Bunuel wrote:
A beaker was filled with a mixture of 40 liters of water and a liquid chemical. They are fixed in the ratio of 3 : 5, respectively. If 2 percent of the initial quantity of water and 5 percent of the initial quantity of liquid chemical evaporated each day during a 10-day period, what percent of the original amount of mixture evaporated during this period?

(A) 22.22%
(B) 33.33%
(C) 38.75%
(D) 44.44%
(E) 58.33%

We can let 3x = the amount of water and 5x = the amount of the liquid chemical originally in the mixture. We create the equation:

3x + 5x = 40

8x = 40

x = 5

So the amount of water originally in the mixture is 3(5) = 15 liters, and the original amount of the liquid chemical in the mixture is 5(5) = 25 liters. Since 20 percent of the initial quantity of water evaporated during a 10-day period, 0.2(15) = 3 liters of water evaporated during this period. Likewise, since 50 percent of the initial quantity of the liquid chemical evaporated during the same period, 0.5(25) = 12.5 liters of liquid chemical evaporated. Therefore, 3 + 12.5 = 15.5 liters of the original 40 liters of the mixture evaporated, which is 15.5/40 = 0.3875 = 38.75% of the mixture.

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Re: A beaker was filled with a mixture of 40 liters of water and a liquid   [#permalink] 02 Oct 2018, 19:50
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