In 70 litres of a mixture of milk and water, the quantity of water is

Question

In 70 litres of a mixture of milk and water, the quantity of water is 10%. How much water should be added so that new mixture may contain 25%.

A. 10
B. 11
C. 12
D. 13
E. 14

KarishmaB · Accepted Answer

Once you get used to this method of solving, you will pretty much be solving this question orally. See if this makes sense:

Solution 1 has 10% water.
Solution 2 has 100% water. (You are mixing solution 1 with pure water.)
Mixture should have 25% water.
w1/w2 = (100 – 25)/(25 – 10) = 75/15 = 5/1
So volume of solution 1 : volume of water = 5:1
Solution 1 is 70 litres, so 14 litres of water must be added.

Bunuel · Answer

Please post answer choices for PS problems. Also make sure you don't reword the questions you post.

As for the question:
There are 10% of water in 70L --> there are 7L of waters;
After x liters of water is added amount of water becomes (7+x) liters, which on the other hand is 1/4th (25%) of new (70+x) liters of mixture: 7+x=1/4*(70+x) --> 28+4x=70+x --> x=14.

Hope it's clear.

MSoS · Answer

70 = 0,1W + 0,9M
Water = 7 Liter

New1: Add x-Liter water to increase W% from 10% to 25%
New2: 
7+x = (70+x)1/4
-42/4 = -3/4x
14 = x

You need to add 14 Liter of Water to get a total of 21 Liter of Water in 84Liter of mixture

Runner2 · Answer

my way
now water is 7/70
it will be (7 +X )/(70 +X ) and it shoud =1/4.
solve and get the answer

LalaB · Answer

first the amount of water was 70*10%=7

(7+x)/(70+x)=1/4
x=14

subhajeet · Answer

In 70 ltr solution we have 63 ltr of milk and 7 ltr of water
now we are adding water but the amount of milk remains constant so (70+x)*75/100 = 63 where x is the amount of water added
on solving x=14

pedroca · Answer

I draw the solution for you (attached). It might help you understand it a bit easier.

fortsill · Answer

(7+x)/(70+x)=1/4
Solve for x; x=14

ENAFEX · Answer

Karishma,

I found your post on mixtures very useful. I am stuck in the above problem. Please help
I solved w1/w2 to be
(90-25)/(25-10) = 65/15.

Can you please explain how you got 75/15?

KarishmaB · Answer

The two mixtures are: a 10% water solution, only water (which is 100% water)
We combine them to get 25% water solution.
Therefore, it is actually (100 - 25)/(25 - 10) and not (90 - 25)/(25 - 10)

Ralphcuisak · Answer

VeritasPrepKarishma , How can we come to know which problems can be solved using the weighted averages formula..Is it applicable to all mixture problems?Or specific ones?

KarishmaB · Answer

For most mixture problems, weighted average formula is quite convenient. Whenever you add two things and consider the final solution or have the final solution and split it into two, weighted averages formula is relevant.

Ralphcuisak · Answer

Thank you for the response Karishma..Will look into the article and implement it for mixture problems..

Andresmadeddie · Answer

90% of milk means 63 litres will remain the same in the final mix. 63 is the 75% of?

63 * 100/75 = 63 * 4/3 = 21 * 4 = 84

Si the final mix will have 84 litres.

84 - 70 = 14

We need to add 14 litres of water

Posted from my mobile device

TheNightKing · Answer

I would use Options.

M=63 W=7

Lets add 13 litres of W. We get 20/83. Nope.

Let's add 14 litres of W. We get 21/84=25%. Answer E. (8.4+8.4+4.2=21)

Codebug4it · Answer

Answer:  Option E

This can be solved quickly using the Weighted Average

70 / W = (100 - 25) / (25 - 20)

=>  W = (70 * 15) / 75 = 14 (E)

anirudh1993 · Answer

Can we use Alligation for this question?

Basshead · Answer

7+X / 70+X = 1/4
70+x = 28 + 4x
42 = 3x
14 = x

Answer is E.

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In 70 litres of a mixture of milk and water, the quantity of water is

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GMAT Problem Solving (PS) Questions

In 70 litres of a mixture of milk and water, the quantity of water is

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