380 is what percent less than 600?

Question

I'm New to percentages and this sum is confusing me a bit. If the question was " 380 is what percent of 600" , I would have converted it to an equation as follows.. 380 = ?% × 600 'n then I could solve it..But here the less than part is confusing me, so thought to post here.. If possible please provide the solution in that equated form so I can better understand 'n appreciate.

Thanking in Advanced..

Answer 1

I agree with the previously given interpretation. To fill in the middle work:

$$380=\frac{x}{100}\cdot 600$$

$$\frac{380\cdot100}{600}=x$$

$$x=63.33%$$.

So $380$ is $63.33^{-}$ percent of 600. But what percent less?

Well $600=100\%$ and $100-63.33^{-}=36.66^{-}$ percent less.

Answer 2

Maybe a possible interpretation is:

$600$ is $100\%$ of $600$ and $380$ is $63\%$ of $600$. So $380$ is $37\%$ less than $600$.

Answer 3

It would be $380=600(100-?\%)$ You are removing $?$ percent of the $600$

Answer 4

The formula for any percent change is: $a = b(1+p)$, where $a$ is the final amount, $b$ the base amount, and $p$ the percent change. In this case:

$a = b(1+p) \Rightarrow 380 = 600(1 + p) \Rightarrow \frac{19}{30} = 1 + p \Rightarrow -\frac{11}{30} = p$.

This indicates that the percentage has decreased by $\frac{11}{30} \approx 0.367 = 36.7\%$.

Answer 5

A good way to approach a problem like this is to start with a little thought experiment: What number is $10\%$ less than $600$? The most sensible answer is $600-60=540$. Turning this around, we can say that $540$ is $10\%$ less than $600$ because

$${600-540\over600}=.1=10\%$$

So it's now a matter of replacing $540$ with $380$:

$${600-380\over600}=.366666\ldots\approx36.67\%$$

Answer 6

The confusion arises from the difference between the parsing of "more than" and "less than", in contrast to the parsing of "percent more than" and "percent less than".

For example: 100 is 20 more than 80, and 80 is 20 less than 100 -- the "more than" and "less than" number expressing the difference between 100 and 80 is the same either way; but 100 is 25 percent more than 80, and 80 is 20 percent less than 100 -- the "percent more than" and "percent less than" numbers are not the same.

Instead of simply being the one number that is equal to the difference between the 2 numbers, they are the two different numbers of hundredths of the 2 different numbers, required for each of the two different aggregates of hundredths to be equal to the one number that is the amount of the difference between the 2 numbers.