explanation please

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

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
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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

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%

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
_________________

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

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:

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

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.