Question

By what percent is 2000 less than 2400? Which one is original amount (2000 or 2400)

Answer 1

Hint: For solving such percent problems in which we had to also know the original amount, then go by step wise step. Follow the question and make points as the question says. As we know that for calculating percent we had to write the value known to be percent divided by original value which is further multiplied by 100 as we will calculate the percent out of 100. So we will do the same here.

Complete step-by-step solution:
So moving further with the question;
Let the 2000 be $x%$ of 2400
So according to question 2000 is $x\%$ less than the 2400. So writing this statement in an equation form we will get;
$\begin{align}
  & 2400-x\% of 2400=2000 \\
 &\Rightarrow 2400-\dfrac{x}{100}\times 2400=2000 \\
 &\Rightarrow 2400-2000=\dfrac{2400x}{100} \\
 &\Rightarrow 400=24x \\
 &\Rightarrow x=\dfrac{400}{24} \\
 &\Rightarrow x=16.67\% \\
\end{align}$
So, 2000 is \[16.67%\] less than 2400.
Hence the answer is \[16.67%\].
Here 2400 is the original amount. As we had calculated by taking the original amount 2400.

Note: keep in mind that while calculating the percent we had multiply by 100 in percent as we did in $x\%$. And follow up the problem step wise step as given, to form an equation. Which will make you solve the questions easily.