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

Question

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%

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

780gmatpossible · Answer

explanation please

dave13 · Answer

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% the closest answer is C

ScottTargetTestPrep · Answer

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.

Answer: C

Jayveelanstr · Answer

If we have 40 Litres, 2:5 means 15L and 25L respectively.

Now 2% of 15L for 10 days means 
2*15*10/100 = 3L

Similarly, 5% of 25L for 10 days means 5*25*10/100 = 12.5L

So total quantity evaporated = 12.5+3 = 15.5L out of 40L total

So (15.5/40)*100 = 38.75%
So the answer is C.

Using this method, it took me 1min, 40 seconds, which is almost half the average time. Hope this helps someone.

Posted from my mobile device

fireagablast · Answer

Given 40L of water and chemical mixed in ratio of 3:5
3x+5x = 40
8x=40
x=5

Water = 3x = 15
Chemical = 5x= 25

Over 10 days, water evaporated 2% everyday and chemical evaporated 5% everyday
10*2% = 20% total evaporated
10*5% = 50% total evaporated

Mixture total = 40
Water evaporated = 15*20% = 3
Chemical evaporated = 25*50% = 12.5
Total evaporated = 12.5+3 = 15.5
% evaporated = 15.5/40 = 38.75%

ScottTargetTestPrep · Answer

Solution:
 
We can create the equation:

3x + 5x = 40

8x = 40

x = 5

Therefore, initially, there are 3(5) = 15 liters of water and 5(5) = 25 liters of liquid chemical in the mixture. During the 10-day period, 20% of the water and 50% of the liquid chemical evaporated, therefore, we are left with 0.2 x 15 = 3 liters of water and 0.5 x 25 = 12.5 liters of liquid chemical evaporated. Therefore, (3 + 12.5)/40 = 15.5/40 = 0.3875 = 38.75% of the mixture evaporated during the 10-day period.

Answer: C

Archit3110 · Answer

solve step by step total given qty ; 40 liters water ; 3/8*40 ; 15 liters and chemical ; 25 liters qty lost 2% water ; so left ; 15*.98 ; 14.7 and 5% chemical so left ; 25*.95 ; 23.75 total solution ; 38.45 evaporated liquid ; 40-38.45 / 40 ; 3.875 % per day and for 10 days it would be 38.75% option C

r532 · Answer

For this problem we can save a few seconds by skipping the calculation to get the value of the multiplier x since the ratios are all we need.

We can then work with 3 for water, 5 for liquid and 8 total, and calculate the amount that evaporates:

\frac{\frac{2}{100}*3*10+\frac{5}{100}*5*10}{8} = \frac{31}{80} =38.75\%

verydisco · Answer

There is no use of the figure of 40 litres of water in this question. We will use only ratios and weighted average to solve this.

Since 2% of water + 5% of chemical evaporate per day for 10 days, and the ratio of water to chemical to total = 3:5:8, we arrive at the following equation.

\frac{(0.02 * 3K + 0.05 * 5K)}{8K}  * 100 * 10 =  \frac{31}{8}  * 10 = 38.75%

It is tempting to convert the ratios into absolute values, i.e., water = 40 L and chemical = 66.67 L, but then further calculations become complex. It's best to convert ratios to absolute values if the figures are convenient. For example, if the ratio of water to chemicals was 2:5, then water = 40 L, chemical = 100 L, which are easy numbers to work with.

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

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