$\frac{3}{8}$ of the inhabitants of the county of North Renfrew and $\frac{1}{40}$ of the inhabitants of South Renfrew live in the biggest town of their county. For every ten people who live in the biggest town of North Renfrew, three people live in the biggest town of South Renfrew. By what percent does the population of South Renfrew exceed the population of North Renfrew?

Correct answer marked below

50%

175%

200%

250%

350%

Correct

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Comments

AnuragMay 18

This one took me way too long. The 'for every ten people... three people' part is where I always mess up the ratio direction.

BrianMay 20

Same here. I had to write it out as 10:3 and then double check which town that actually referred to.

SantiagoMay 27

Yeah the wording is sneaky. I initially set it up backwards and got a nonsense answer.

IwinosaMay 18

705-805 seems right, this is not a plug-in friendly problem. I ended up with fractional populations and had to trust the algebra.

ShivangiMay 22

Exactly, I kept trying to pick smart numbers but the 1/40 made it ugly.

XanJul 11

Quick thanks, the key for me was turning the sentence into an equation instead of eyeballing it. Once N and S were defined clearly it fell out.

AnJul 14

Defining the variables is half the battle on these percentage translation problems.

NavneetJul 15

Is it just me or is 'by what percent does South exceed North' different from 'what percent of North is South'? I feel like that's where the trap is.

What this question tests

Your ability to compute percentage change, percentage of a whole, and to work backwards from a final value.

Treating successive percentage changes as additive — a 10% rise then a 10% fall is not back to the start.