Question

A potato seller sells $ 70\% $ of the total potatoes and still has $ 150kg $ potatoes left with him. Find the weight of potatoes he had originally.

Answer 1

Hint: We will assume the original amount of potatoes ‘x’, and find out $ 30\% $ of ‘x’ which is the remaining with the seller equal to $ 150kg $ . Which will ultimately give us the value of ‘x’ which is the original amount of potatoes.

Complete step by step answer:
Moving ahead with the question in step wise manner;
Let the amount of total potatoes seller initially have $ =x $
According to the question seller had sold out $ 70\% $ potatoes in total, as we know that there are a total $ 100\% $ potatoes. So the remaining potatoes that seller has will be the total percent of potatoes subtracted with the percent of potatoes the seller had sold out. So it would be;
 $ 100\%-70\%=30\% $
So $ 30\% $ is the percentage of potatoes the seller still has. And according to the question the amount of potatoes the seller still has after selling $ 70\% $ is $ 150kg $ . Which means $ 30\% $ of ‘x’ is equal to $ 150kg $ , i.e.
 $ 30\% $ of $ x=150kg $
So as we know that to calculate the percent, we need to divide percent by 100 in order to remove percent sign and replace ‘of’ with multiplication. So we will get;
 $ 30\% $ of $ x=150kg $
\[\begin{align}
  & \dfrac{30}{100}\times x=150kg \\
 & \dfrac{30x}{100}=150kg \\
\end{align}\]
As in this equation we have one variable i.e. ‘x’. To find it out just simplify the equation, so we will get;
\[\begin{align}
  & \dfrac{30x}{100}=150kg \\
 & 30x=15000kg \\
 & x=\dfrac{15000kg}{30} \\
 & x=500kg \\
\end{align}\]
So we got ‘x’ equal to \[500kg\], as ‘x’ is the total amount of potatoes that seller had initially, so we can say that \[500kg\] is the amount of potatoes the seller had originally.
Hence the answer is \[500kg\].

Note: Rather than finding the remaining percent, which we got $ 30\% $ you can also go with the $ 70\% $ . But with it there will be a slight change in the equation, as $ 150kg $ is the amount of remaining potatoes, so we can write it as when $ 70\% $ of original amount got sold out then the remaining will be $ 150kg $ . So we will get equation
$\begin{align}
  & x-70\% of ‘x'=150kg \\
 & x-\left( \dfrac{70}{100}\times x \right)=150kg \\
\end{align}$.
From both ways you will get the same answer.