Fraction of the solution that was replaced

[Vemuri]

A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?

(A) 1/4

(B) 1/3

(C) 1/2

(D) 2/3

(E) 3/4

[mals24]

Let x be the quantity of 40% solution that was replaced by 25% solution.

The new concentration is now 35%

35% includes 'x' quantity of 25% solution and remaining quantity of 40% solution.

Remaining quantity = total quantity - x
where total quantity = 1 (since in fractions the total is 1)

Remaining quantity = 1-x

Equation: X*25% + (1-X)*40% = 35%
X = 5/15 = 1/3

Answer is B

[Vemuri]

Cool explanation mals4. Thank you

[kapsii]

If you can get your head around this explanation, perhaps it will save you a lot of time in writing equations (and also lessen your chances of making a stupid mistake!).

Argument:
Acute observation of averages tells us:
Total loss/gain of a quantity as a result of addition/removal/replacement to/from the original set, must be equal to the total change in the quantity.

Loss/gain = number of parts impacted * (deviation from the earlier average).

Total change in quantity = |(New average - Old average)| * total number of parts.

Looking at the question in this thread:
solution having 25% strength replaced x parts of solution having 40% strength, thus total loss = (40-25)*x

Total change in quantity = (40 - 35) * 1 (1 because we are finding the fraction, 100 if we want the percentage and so on...)

So, as we are reading the question, with practice we should be able to write 15x = 5 on the scratch pad almost instantaneously.

Rest is arithmetic...

This type of question can come in various formats, but almost always only one part of the equation would be missing, it could be the total change in quantity, or the new average, or as it was here, change in number of parts...

HTH