which batch to make 60...ambiguity in question

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.

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

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

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
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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
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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

Is it only me who got confused by the wordings?

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