A company produces a cleaning solution that has 60% concentration of C

Question

A company produces a cleaning solution that has 60% concentration of Chemical K. The current production batch contains 200L of an ingredient with a 30% concentration of Chemical K and 150L of an ingredient with a 40% concentration of Chemical K. How much pure chemical K must be added to the batch to attain the correct concentration of Chemical K?

A. 150L
B. 175L
C. 200L
D. 225L
E. 250L

A. 150L
B. 175L
C. 200L
D. 225L
E. 250L

prashanths · Accepted Answer

30% of 200 = 60L of K
40% of 150 = 60L of K

120L/350L

(120 + x)/(350 + x) = 60% = 3/5

600 + 5x = 1050 + 3x
2x = 450
x = 225

225L of K to be added.

Option D.

yogi02 · Answer

which batch to make 60...ambiguity in question

MahmoudFawzy · Answer

in the premise, one batch is mentioned,
and that batch is formed of adding two different concentrations: 200L of 30% K and 150L of 40% K

Conc. 1: 
K:Water:total
30:70:100 (ratio)
60:140:200 (L)

Conc. 2: 
K:Water:total
40:60:100 (ratio)
60:90:150 (L)

so by adding, K:Water:total = 120:230:350 (L) --> which is the final form of the current batch

to convert it to 60% by adding x (L) of K,
 \frac{120+x}{350+x}  =  \frac{60}{100} ,
and x = 225L

lacktutor · Answer

200*30%=60L chemical K
150*40%=60L chemical K
200+150=350L (concentration)

—> 60+60=120L —chemical K
350–120=230L —water

If you add the pure chemical K, the amount of total water cannot be changed in the concentration.
 —> according to the question, the amount of water should be 40%:

230–>40%
x—> 100%

—> x= 100*230/40= 23*25=575
575–350=225L (pure chemical K)

The answer choice is D.

Posted from my mobile device

ScottTargetTestPrep · Answer

We can create the equation:

(200 x 0.3 + 150 x 0.4 + K)/(350 + K) = 0.6

(60 + 60 + K)/(350 + K) = 3/5

5(120 + K) = 1050 + 3K

600 + 5K = 1050 + 3K

2K = 450

K = 225

Alternate Solution:

We have 200 liters of 30% solution and 150 liters of 40% solution, and we will add x liters of 100% solution, thus obtaining (200 + 150 + x) liters of a 60% solution. We can summarize this in the following equation:

200(0.30) + 150(0.40) + x(1.00) = (200 + 150 + x)(0.60)

60 + 60 + x = 120 + 90 + 0.6x

120 + x = 210 + 0.6x

0.4x = 90

x = 225 liters

Answer: D

rohit8865 · Answer

200L of an ingredient with a 30% concentration of Chemical K = 30%of 200 = 60L
and 150L of an ingredient with a 40% concentration of Chemical K = 40% of 150 = 60L
 _______
 Total of Chemical K = 120L

And Total solution is now = 200L + 150L =350L
Now let X amount of Chemical K is added to above 120L of Chemical K ,which is required to be 60% of total solution

120+X = 60% of (350 + X) 
120 + X = 3(350+X)/5
600 + 5X =1050+3X
2X= 450
X= 225L

Ans D

PinakiRDas · Answer

Is it only me who got confused by the wordings?

adityasuresh · Answer

A company produces a cleaning solution that has 60% concentration of Chemical K. The current production batch contains 200L of an ingredient with a 30% concentration of Chemical K and 150L of an ingredient with a 40% concentration of Chemical K. How much pure chemical K must be added to the batch to attain the correct concentration of Chemical K?

A. 150L
B. 175L
C. 200L
D. 225L
E. 250L

A. 150L
B. 175L
C. 200L
D. 225L
E. 250L

Weighted Average formula for Mixtures :  A2 - Aavg/Aavg - A1 
A1 = 200 *  30/100  (stem: first part of current batch) +  40/100  * 150. (2nd part of current batch)
Percentage of Chemical K in current batch =  120/350  * 100 =2 40/7  = A1 (Approx 34)
W1 = Weight of current batch = 200 + 150 = 350
A2 = % of chemical k in pure chemical k = 100 
W2 = ?
Therefore substituting values.
 350/W2  =  100 - 60/60 - 34 
 350/W2  =  40/26 
4550 = 20W2
Therefore W2 = 225
 D

A2D2 · Answer

Can someone pls tell why this method is wrong and is there a concept error

divyadna · Answer

Posted from my mobile device

Charleeagni · Answer

If I had a dollar for every question like this I have solved, I would have, wait, what was the question again?

egmat · Answer

Step 1: Calculate the Chemical K we currently have 
From the  200L  batch at 30% concentration:
Chemical K = 200 × 0.30 =  60L

From the  150L  batch at 40% concentration:
Chemical K = 150 × 0.40 =  60L

Total Chemical K currently = 60 + 60 =  120L  
 Total volume currently = 200 + 150 =  350L

Step 2: Set up the equation 
Let  x  = liters of pure Chemical K to add

When you add pure Chemical K, it adds to BOTH the numerator AND the denominator!

After adding x liters of pure Chemical K:
- Total Chemical K = 120 + x
- Total volume = 350 + x (this is the part many students miss!)

For 60% concentration:
(120 + x) / (350 + x) = 0.60

Step 3: Solve 
120 + x = 0.60 × (350 + x)
120 + x = 210 + 0.60x
x - 0.60x = 210 - 120
0.40x = 90
x =  225L

Answer: D

egmat · Answer

Step 1: Calculate the Chemical K we currently have 
From the  200L  batch at 30% concentration:
Chemical K = 200 × 0.30 =  60L

From the  150L  batch at 40% concentration:
Chemical K = 150 × 0.40 =  60L

Total Chemical K currently = 60 + 60 =  120L  
 Total volume currently = 200 + 150 =  350L

Step 2: Set up the equation 
Let  x  = liters of pure Chemical K to add

When you add pure Chemical K, it adds to BOTH the numerator AND the denominator!

After adding x liters of pure Chemical K:
- Total Chemical K = 120 + x
- Total volume = 350 + x (this is the part many students miss!)

For 60% concentration:
(120 + x) / (350 + x) = 0.60

Step 3: Solve 
120 + x = 0.60 × (350 + x)
120 + x = 210 + 0.60x
x - 0.60x = 210 - 120
0.40x = 90
x =  225L

Answer: D

SubaitaS · Answer

I did the same thing, did you get why it's giving the wrong answer? If yes, please share the reason, thanks!

A company produces a cleaning solution that has 60% concentration of C

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