Bit tricky plot on GRE > In a city **_90%_** of the population own a car, **_15%_** own a motor cycle, and everybody owns one or the other or both. Find the percentage of motorcycle owners to car owners. In order to solve it i have first found out that **_5%_** are the guys `who owns owns one or the other or both`. Now I require, `Find the percentage of motorcycle owners to car owners.` I have added for car-ians : $90\,\% + 5\,\%=95\,\%$. And motorcycl-ians: $15\,\% +5\,\%=20\,\%$. Found out the ratio as $4:19$ but found it incorrect. why?

Good try, but you zigged when you should have zagged.

$90\%$ own a car, but some might also own a motorcycle. $15\%$ own a motorcycle, but some might also own a car.

It is correct that $5\%$ own both. But that means that $85\%$ own _only_ a car, and $10\%$ own _only_ a motorcycle. Those add up to $100\%$, as they should.

If you're looking for the ratio of motorcycle-only owners to car-only owners, it's $10/85 = 2/17.$

If you're looking for the ratio of motorcycle owners to car owners (regardless of whether or not they own both) it's $15/90 = 1/6$.