A 120-milliliter mixture of Chemical X and water contained 40 percent

Question

A 120-milliliter mixture of Chemical X and water contained 40 percent Chemical X. A part of the mixture was removed and replaced with an equal quantity of water. If the resulting mixture contained 10 percent Chemical X, what is the volume of the mixture that was removed?

A. 80

B. 82

C. 84

D. 88

E. 90

A. 80

B. 82

C. 84

D. 88

E. 90

Archit3110 · Answer

total mix 120 ml
removal gives 120* .1 ; 12 ml mixture
.4*(120-x) = 12
48-.4x=12
-.4x=-36
x= 90
option E

jdcsantos · Answer

2/5 of 120 = 48ml of Chemical X

if Chemical X = 10% after removing and replacing the mixture (keeping same amount) x = 12
:. 36ml of X was replaced by water
multiplying by the reciprocal of 2/5 -> 5/2 we get
x = 36 * 5/2
x = 90

Option E

HEPENNYPECKER · Answer

120/48 - x*2/5 = 100/10

solve for x, x = 90 mL

Mohammadmo · Answer

0.4×120=48milliliters of chemical X.
So (48_0.4x)/120 = 1/10
4x=360
==»x=90
Option E

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vassspire · Answer

Can someone please post a better explanation for this problem?

ThatDudeKnows · Answer

vassspire

We start with 40% X, which is 48mL.
We want to remove enough X to get to 10% X, which is 12mL.
That means we need to remove 36mL X.
What volume (V) of the mixture needs to be removed in order to remove 36mL X?
0.4(V)=36
V=36/0.4=90

Answer choice E.

GM2021 · Answer

Using allegations

0 ( water which is mixed contains 0 % chemical) —— 10% ——-40%
so quanities mixed are in ratio

40-10:10-0 >>> 3:1 so qty of water = 
3/4*120 = 90 ml

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FlyingMAK · Answer

I understand the computation, I just don’t understand the logic. Can you please elaborate on the logic

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Ishmeet7 · Answer

None of the solutions have explained the answer properly. Can someone please draw the mixture diagram and share the answer here?

youcouldsailaway · Answer

The problem can be solved using allegation method and by using respective percentages of chemical X in each type of liquid / soln.

One note - I was struggling on the last part, i.e, what should we multiply the ratio with but then I realized that  a part of the solution was removed and was then replaced with an equal part . It's basically saying that out of a bag of 5 candies, one was removed and another was placed instead; in the end we will still have 5 candies in the bag! Same way, here the final solution will be of 120 ml only.

JeffTargetTestPrep · Answer

The percentage of Chemical X in the resulting mixture can be expressed as the weighted average of the percentages of Chemical X in the components of the resulting mixture.

If y milliliter is exchanged with water, we have:

/120 = 10
(120 – y)(40) = 1,200
480 – 4y = 120
360 = 4y
y = 90

Answer: E

Mgerman42 · Answer

This explanation is still unclear. I think the only difficult part is why are you take 36/.4? 36ml seems like it is already the volume removed. Why does dividing by 40% actually represent the volume removed? Idk where in the wording of the question I can't pick up on this but seems to me like the answer should just be 36ml. Probably why I absolutely suck at this test.

riteshcasper · Answer

Think of it this way, if you a mixture of 2 products, X and water in this case, you can't simply remove chemical X from the water based mixture. You will always change the ratio by diluting the mixture with water to reduce the % of chemical X. In this case you know you need to remove 36ml of chemical X from the existing mixture to arrive at new ratio of 10%.

To do this, you will remove 36ml/40% = 90ml of the entire mixture from the vessel, then add equivalent amount of water to arrive at the desired ratio.

ani199411 · Answer

horrific explainations!

Adit_ · Answer

Initially from 48ml chemical X has no changed to just 12ml
36ml has been removed
or
36=2/5x
x=90

Answer:  Option E

A 120-milliliter mixture of Chemical X and water contained 40 percent

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A 120-milliliter mixture of Chemical X and water contained 40 percent

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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