Question

Aaron had Rs.2100 left after spending 30% of the money he took for shopping. How much money did he take along with him?
(a) Rs.2000
(b) Rs.7000
(c) Rs.3000
(d) Rs.210

Answer 1

Hint: To solve this problem we need to first know that how to find the X% of a quantity Y. X% of the Y would be given as $X\%\,of\,Y\,=\dfrac{X}{100}\times Y$. So in this question first we will assume the money that Aaron took with him equal to a random variable say Rs.X and after that we will calculate the 30% of that money and then subtract it from the total money and then we will equate it with Rs.2100 to get the value of X. and value of X will be our required answer.

Complete step by step answer:
We are given that Aaron spent 30% of the money he took with him and after that he is left with Rs.2100, so
To solve this problem, we should know that what is the meaning of percentage,
Y% Percentage is defined as the Y parts per hundred parts of the given quantity.
And Y% of the Z amount is given by = $\dfrac{Y}{100}\times Z$
Now for this question we will first find out the 30% of the money that Aaron took for but before that let us assume the total money that he took as Rs.X, so we get
30% of Rs.X as,
$\begin{align}
  & =30\%\,of\,Rs.X \\
 & =\dfrac{30}{100}\times X \\
 & =\dfrac{3}{10}X \\
\end{align}$
Now money that he is left with after spending 30% of total will be given by,
$\begin{align}
  & =X-\left( 30\%\,of\,Rs.X \right) \\
 & =X-\dfrac{3}{10}X \\
\end{align}$
Now equating this with the given amount that he is left with. we get,
$X-\dfrac{3}{10}X=2100$
Taking LCM, we get
$\begin{align}
  & \Rightarrow \dfrac{10X-3X}{10}=2100 \\
 & \Rightarrow \dfrac{7}{10}X=2100 \\
\end{align}$
Cross multiplying we get,
$\begin{align}
  & \Rightarrow X=2100\times \dfrac{10}{7} \\
 & \Rightarrow X=3000 \\
\end{align}$
Hence the total money that Aaron took with him for shopping is Rs.3000

So, the correct answer is “Option C”.

Note: To solve these kinds of problems you should have prior knowledge of how to calculate the percentage so remember the mentioned formulas in the solution to find percentage. And also some students might just equate the 30% of the total money with the given left amount but it is wrong as it is the left amount which we are given in the question so we need to subtract it from total money to get the desired result so try to read the question carefully and then solve it.