Averages Question

[sukhman]

There is a 60 litre solution of milk and water in which milk forms 84% . How much water must be added to this solution to make it a solution in which milk forms 64 % . Sorry No choices but I have seen these types of questions in GMAT .

[Uva@90]

There is a 60 litre solution of milk and water in which milk forms 84% . How much water must be added to this solution to make it a solution in which milk forms 64 % . Sorry No choices but I have seen these types of questions in GMAT .

Sukhman

Is OA 18.75 ?

Here is how I did,

Let X be the amount of water to be added.

Liter's Solution ----%Milk--- Total Liters of milk


60-------------------- 84 ------ = 60*(84/100)
60+X-------------------64------- =(60+X)*(64/100)

So, (60+X)*(64/100) = (60)* (84/100) , Solve for X
You will end with X = 18.75.

Experts Correct me if I am wrong.

Regards,
Uva.

Edited - Did calculations Wrong, now it is perfect.

[sukhman]

Its Actually 18.75.

[Uva@90]

Its Actually 18.75.

Ya you are right it is 18.75 only I made mistake in calculations.

(God!!! When I will over come doing mistake in calculations.. )

Regards,
Uva.

[Brent@GMATPrepNow]

There is a 60 litre solution of milk and water in which milk forms 84% . How much water must be added to this solution to make it a solution in which milk forms 64 %

I often find it useful to sketch the mixtures with the individual components separated. This allows me to see exactly what's happening.
So, we have a 60 ml solution that is 84% milk.
84% of 60 = 50.4 ml, so we have 50.4ml of milk and 9.6ml of water.
From here, we get . . .


Cheers,
Brent

[GMATGuruNY]

There is a 60 litre solution of milk and water in which milk forms 84% . How much water must be added to this solution to make it a solution in which milk forms 64 % . Sorry No choices but I have seen these types of questions in GMAT .

Amount of milk in the original solution = .84(60) = 50.4 liters.
These 50.4 liters must constitute 64% of the altered solution:
50.4 = .64x
x = 50.4/.64 = 5040/64 = 630/8 = 315/4 = 78.75.

Since the new volume = 78.75, and the original volume = 60, the amount of added water = 78.75 - 60 = 18.75 liters.