A certain quantity of $40%$ concentration solution is replaced with $25%$ concentration solution such that the concentration of the combined amount is $35%$ . What’s the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?

Answer Choices

Correct answer marked below

1:3

1:2

Correct

2:3

2:1

3:1

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Comments

ShimantaApr 18

Got 1:2 pretty quickly. Used alligation: 40% and 25% give 35%, so ratio of final amounts is 1:1. Since the 25% part is the replaced amount and the 40% part is what remains, the replaced to not replaced is 1:1? Wait, but that's not an option. Hmm, I must be mixing up. Let me redo: alligation says the ratio of the 40% solution to the 25% solution in the final mixture is (35-25):(40-35)=10:5=2:1. So the remaining 40% is twice the added 25%. Thus replaced:not replaced = 1:2. Answer B. That was tricky because the replaced amount is removed and replaced, so the final 40% amount equals the not replaced amount. Good question.

PrajwalMay 1

Nice, I fell for the same trap initially. The key is that after removing some 40% and adding 25%, the amount of 40% left is exactly the not replaced amount.

AndrésApr 19

Exactly. Alligation gives the ratio of the two components in the final mixture, not the ratio of replaced to not replaced. That extra step is what makes it a 655-705 level.

VanyaJun 10

Is there a way to do this without alligation? I set up x as replaced amount, V as total original volume. Then final concentration: (0.4(V-x)+0.25x)/V = 0.35. Solve: 0.4V -0.4x +0.25x =0.35V => 0.05V =0.15x => x/V =1/3. But x/V is replaced/total, so replaced/not replaced = x/(V-x) = (1/3)/(2/3)=1/2. That matches B. But it took me a while to set up correctly.

BerkayJun 16

Your algebra is clean. I like that you defined V as total original volume and then found x/V first. That avoids the common mistake of thinking x/V is the answer.

SrushtiApr 26

This one took me 3 minutes because I kept second-guessing. The wording 'replaced with' is key: you remove some of the original 40% and put in 25%. The amount removed equals the amount added. So the final 40% amount is the original minus removed. Alligation is faster but I always mix up which side corresponds to which. Any mnemonic?

ArnauApr 30

I remember: the stronger solution is further from the final percentage, so it gets the smaller share. Here 40% is 5 away from 35%, 25% is 10 away. So 40%:25% = 10:5 = 2:1. That means the 40% (remaining) is twice the 25% (added). So replaced:not replaced = 1:2.

ConradoApr 30

Thanks, that mnemonic helps. I'll try to remember 'distance is inverse to amount'.

What this question tests

What it tests

Your ability to reason about weighted averages and the composition of mixtures.

Common trap

Averaging the percentages of two solutions without weighting by their volumes.

A certain quantity of 4040%40 concentration solution is replaced with 2525%25 concentration solution such that the concentration of the combined amount is 3535%35. What’s the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?