Mixtures

[ibelieveican]

A substance is 99% water. Some water evaporates, leaving a substance

that is 98% water. How much of the water evaporated?

[ibelieveican]

My approach

 

let there be 1% alcohol

Let the volume be 100x

 

99x water 1x alcholol

let the new volume be 100y

 

98y water and 2y alchol

 

now we know that water evaporated so this gives the volume of alchohol remains the same.

so 1x= 2y

x = 2y

 

water evaporated is 99x-98y = 49x

 

But the answer is

50.5%

 

[Shooter]

water evaporated is 99x-98y = 50x not 49x

50% of x

 

but still we are not appropriate.

[ibelieveican]

water evaporated is 99x-98y = 50x not 49x

50% of x

 

but still we are not appropriate.

Thanks shooter..

yeah it should be 50x

[ramzrambo]

Let the two substances be w (water) and a

 

now acc to ques: case 1) w1/a1 = 99/1

==> a1 = w1/99

 

where w1 is water initially.

case 2) w2/a2 = 98/2

==> a2 = w2/49...(where w2 is water in second case)

now a1 = a2

 

w1/99 = w2/49

==> w2 = 0.495w1

 

hence water remaining in second case id 0.495 times that of W1

wayer evaporated = w1 - w2 = w1 - 0.495w1 = 0.505 w1

50.5%, hence is the amount of water that evaporated.

[ibelieveican]

Thanks buddy...

I got your point but i think I am missing a concept somewhere.. could you tell me what went wrong with my approach

[ibelieveican]

my mistake.. i got it..

the % evaporated is 50/99 which is 50.5%

 

silly percent pbl :(

[mail2jkd]

Let us assume the water is 99 parts and substance is 1

 

The water evaporates and the 1% substance becomes 2%, i.e 1 becomes 2% of the mixture.

 

Let us assume the new mixture volume is x, which can be expressed as

(1/x)*100 = 2

2x=100

x=50

The new mixture is 50 parts with 49parts water and 1 part substance.

 

The evaporated water percent = (99-49)/99 = 50/99 = 50.5%

[bose]

tricky question,

percent of water evaporated to be calculated of the intial water content and not the whole substance. so ans 50.5%

[vijay1311]

Let there be a total of 100 Litres of the solution. which contains 1 part as substance and 99 parts water.

Let a parts of water is evaporated, then the resulting solution has (100-a) litres of water.

 

Now (99% of 100) - a =98% (100-a)

--> 99 - a = 98 - 98a

--> 1 = 2a -->a=50

i-e 50 parts of the initial total amount(100) is evaporated or 50 parts of initial water content(99)=50.5 is evaporated.

Edited September 12, 2010 by vijay1311

[solmon]

Here is my approach.

 

Initial water 99/100 ; after evaporation 99-x/100-x =98/100 =>

9900-100x=9800-98x =>100=2x => x=50 (substance of water evaporated)

50/99 will give you percent of water evaporated.