Question

A vegetable seller had some carrots. She sells 60% of the carrots and still has 300 carrots left. How many carrots did she have at the beginning?

Answer 1

Hint: In the above question, first of all we will suppose the number of carrots at beginning to be variable and then, we will subtract 60% of the carrots at beginning which is equal to the carrots that are left with us.

Complete step-by-step answer:
We have been given that, a vegetable seller had some carrots. She sells 60% of the carrots and still has 300 carrots left. So, we have to find the carrots that she has at the beginning.
Let us suppose, the number of carrots at the beginning to be x.
Now, 60% of the carrots \[\begin{align}
  & \Rightarrow 60\%\text{ of x} \\
 & \Rightarrow \dfrac{60}{100}\times x\text{ = }\dfrac{3x}{5} \\
\end{align}\]
According to the question, we have,
\[x-\dfrac{3x}{5}=300\]
On taking LCM of the terms, we get:
\[\begin{align}
  & \Rightarrow \dfrac{5x-3x}{5}=300 \\
 & \Rightarrow \dfrac{2x}{5}=300 \\
\end{align}\]
On multiplying the equation by \[\dfrac{5}{2}\] to both sides, we get:
\[\begin{align}
  & \Rightarrow \dfrac{5}{2}\times \dfrac{2x}{5}=\dfrac{5}{2}\times 300 \\
 & \Rightarrow x=450 \\
\end{align}\]
Therefore, the number of carrots that the seller has at the beginning is equal to 450.

Note: In general, we made a mistake in the given question is that, we just find the 60% of the number of carrots at the beginning and equate it to 300 but it is incorrect and thus gives a wrong answer because 60% of the carrots are sold by the seller and 300 is the number of carrots left after selling. So, we must subtract 60% of the number of carrots from the number of carrots at the beginning which will be equal to 300.