100 liters of 20% alcohol is mixed with x liters of x% alcohol to give

Question

100 liters of 20% alcohol is mixed with x liters of x% alcohol to give a mixture that contains at least 35% alcohol. What is the minimum value x can take?
A. 100 liters
B. 80 liters
C. 60 liters
D. 50 liters
E. 40 liters

CareerGeek · Answer

100*20/100 + x*x/100 ≥ (100+x)*35/100
—> 20 + x^2/100 ≥ 35 + 35x/100
—> x^2 - 35x - 1500 ≥ 0
—> (x - 60)(x + 25) ≥ 0
Solution is x ≤ -25 or x ≥ 60 
Minimum value of x is 60 (since c cannot be negative)

IMO Option C

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SanjayNR · Answer

Currently we have 20% of 100 liters alcohol = 20 liters alcohol in 100 liter solution.

Now we need atleast 35% in total and % alcohol= number of liters of alcohol added.

First take D. 50 liters:
50% of 50 liters = 25 liters

Total liters of solution = 100+50 = 150. 
Total liters of alcohol = 20+25 = 45.

45/150<35% - so eliminate D and E also (since E will definitely be lesser than 35% if even lesser % of solution is alcohol)

Now we need to check C:

60% of 60 = 36

total liters of alcohol =20+36=56

total liters of solution = 100+60 = 160

56/160= 7/20 = 35% exactly.

So now we can eliminate D & E since all we need is the minimum value of X

X=60

Hence C is the answer

ScottTargetTestPrep · Answer

We can create the inequality:

100 * 0.2 + x * x/100 ≥ 0.35(100 + x)

20 + x^2/100 ≥ 35 + 0.35x

x^2/100 ≥ 15 + 0.35x

x^2 ≥ 1500 + 35x

x^2 - 35x - 1500 ≥ 0

(x + 25)(x - 60) ≥ 0

If this were an equation, we would have -25 or 60 as the solutions. Of course, x can’t be negative, so x = 60 is the only value that would make the expression (x + 25)(x - 60) equal to 0. If x > 60, the expression would be greater than 0. Therefore, x is at least 60, so its minimum value is 60 liters.

Answer: C

chrtpmdr · Answer

I dont get this problem, these values could all be the right answers. 
100 liters of 20% alcohol are mixed with x liters of x% alcohol

So we neither know the added liters nor the % of the added liters. What is the MINIMUM value x can take to give a solution that contains at least 35% alcohol.

Say 40 liters is a 100% solution

100 + 40 = 140 liters 
20 + 40 alcohol

60/140 > 0.35 ; possible

KSBGC · Answer

we can alligation method here

20.................x%

35

35 - x 15

we got the ratio here .

15 reflects the x liters portion

only 60 is basically the multiple of 15.......

Best answer is C

shubhagata94 · Answer

VeritasKarishma  Can you help solve this using the w1/w2 method or the scaling method? I can't seem to do it.

KarishmaB · Answer

Yes, we can use scale method for most mixture problems. We need the minimum value of x to get at least 35% concentration. The lesser the value of x, the lower the overall concentration. Hence, the lowest value of x will be obtained when concentration is 35% and not higher than that.

w1/w2 = (A2 - Aavg)/(Aavg - A1)

100/x = (x - 35)/(35 - 20)

1500 = x(x - 35)

At this point, we can plug in the values to see what will work. x = 60 works.

shubhagatac94 · Answer

I understood your solution. I have one question. When the new solution is 35%, isn’t the total solution 100+x litres? So, why isn’t w1/w2 = (100/100+x)?

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100 liters of 20% alcohol is mixed with x liters of x% alcohol to give

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100 liters of 20% alcohol is mixed with x liters of x% alcohol to give

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