A merchant is trying to make lemonade with 20% lemon juice but he has

Question

A merchant is trying to make lemonade with 20% lemon juice but he has added too much lemon juice and now has 4 liters of a solution that is 55% lemon juice. How much water does he have to add to make the solution the correct strength?

A. 1.4 liters
B. 1.75 liters
C. 2.5 liters
D. 5.4 liters
E. 7 liters

A. 1.4 liters
B. 1.75 liters
C. 2.5 liters
D. 5.4 liters
E. 7 liters

GMATinsight · Accepted Answer

Amount of lemon in 4 litres of solution = 55% of 4 lts = (55/100)*4 = 2.2 Litres

Now the needed percentage of Lemon = 20%

i.e. 2.2 should serve the purpose of 20% of the total solution

i.e. (20/100)*Total Solution = 2.2

i.e. Total Solution = 11 Litres

so the water that needs to be added = 11 - 4 = 7 Litres

Answer: Option E

mohshu · Answer

GMATinsight  
can we solve this using weighted average formula

VeritasPrepKarishma  plz help

GMATinsight · Answer

Here it is

4 Lts solution has 55% lemon and x Lts water to be added has zero percentage lemon so the equation becomes

/ (4+x) = (20/100)

I.e. (55/100)*4 + (0/100)*x = (20/100)*(4+x)

Solving this we get x = 7 Lts.

I hope this helps.

Posted from my mobile device

gracie · Answer

let w=liters of water to be added
.55*4=.2(4+w)
w=7 liters
E

gjonrexha · Answer

First step convert into a fraction.
55% = 22/40 --> Every Liter is a denominator of 10.
Second step divide 22 by .2.
22/.2 --> 110 is the new denominator.
Third step subtract 110 by 40.
110-40 = 70 which equals 7 liters

Sent from my iPhone using GMAT Club Forum mobile app

laddaboy · Answer

20 % is 1/5th of solution.

We have 4 Liters of Solution which has 2.2 Liters(55%) of Lemonade and 3.8 Liters of water.

Need to add x liters of water so that the lemonade becomes 1/5th of the new solution.

Hence for new solution 4+x liters will have 2.2 Liters of Lemonade and 3.8+x liters of water. Now 2.2 liters should be equal to 1/5th of 4+x liters .

So E.

laddaboy · Answer

20 % is 1/5th of solution.

We have 4 Liters of Solution which has 2.2 Liters(55%) of Lemonade and 3.8 Liters of water.

Need to add x liters of water so that the lemonade becomes 1/5th of the new solution.

Hence for new solution 4+x liters will have 2.2 Liters of Lemonade and 3.8+x liters of water. Now 2.2 liters should be equal to 1/5th of 4+x liters .

So E.

Badari · Answer

Amount of lemon in 4 litres of solution = 55% of 4 lts = (55/100)*4 = 2.2 Litres

Amount of water in 4 litres of solution = 45% of 4 lts = (45/100)*4 = 1.8 Litres

Now the needed percentage of Lemon = 20%

i.e. 80% of the total solution will now have water. Ratio of Lemon and water now stands as (1:4)

Let us assume that  X liters  of water is added to arrive at this ratio:

So, 2.2/(x+1.8) = 1:4

i.e. X = 7 liters.

so the water that needs to be added = 7 Litres

Answer: Option E 
_________________

JeffTargetTestPrep · Answer

Since the merchant has 4 liters of a solution with 55% lemon juice, he has 0.55 x 4 = 2.2 liters of pure lemon juice.

We must determine how many liters of water must be added to make the solution 20% pure lemon juice.

lemon juice/total = 20% = 1/5

We can let w = the amount of water in liters that should be added to the solution. Thus:

2.2/(w + 4) = 1/5

2.2 x 5 = w + 4

11 = w + 4

7 = w

Answer: E

sasyaharry · Answer

The question comes down to how much water should be added to increase the % of water from 45% to 80%.

0.45(4) + x = 0.80(4+x)

1.8 + x = 3.2 + 0.8x

0.2x = 1.4

x = 7

Hence, 7 liters of water must be added to increase the water content from 45% to 80%.

gps5441 · Answer

W1/W2=(A2-avg)/(avg-A1)

W1=water
W2=Lemon Juice
A2=55(lemon Juice)
A1=0(Water)
Avg=20(Required Concentration)
W1/W2=(55-20)/(20-0)=35/20=7/4 ie total sol =7+4=7 liters of water

Varun121595 · Answer

Alternative way:
1.8 + x/ 4 + x = 80/100 
Solve x for water required.

FlyingCycle · Answer

not sure why nobody uses Cf = Ci * (Vi/Vf) formula. It works so smooth and gives the answer within second.

Cf = Ci * (Vi/Vf)
20 = 55 * (4/Vf)
Solving this, we get Vf as 11, then we need to subtract 4 from it which gives us 7.

Basshead · Answer

55 - 20 / 20 - 0 = 7/4

We have 4 liters; we need another 7 liters to achieve 20% lemon juice.

ASR2021 · Answer

Lemon - 0.55
Water - 0.45
Lts - 4
Required concentration = 0.20

0.55(4-x) + 0.45x = 0.8
Solving x = 14

Please someone correct me. What is it that I am doing wrong?
The alignment is a mess. It is basically the table method.

bumpbot · Answer

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A merchant is trying to make lemonade with 20% lemon juice but he has

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