Question

Ramu sold a plot of land for Rs2,40,000 gaining 20%. For how much did he purchase the plot?

Answer 1

Hint: In this question, we need to first find the value of that 20% in 2,40,000. Then subtract that percentage value from the total value of 2,40,00 which gives us the cost at which he purchased the plot.

Percentage formula is given by:
\[\dfrac{x}{100}\times y\]

Complete step-by-step answer:

Let us look at some of the basic definitions.
PERCENTAGE: The word 'percent' means 'per hundred' or 'out of hundred', symbol % is used to express the percentage.
To convert a fraction into percentage multiply the fraction by 100.
If fraction is \[\frac{x}{y}\], then its percentage is \[\left( \dfrac{x}{y}\times 100 \right)%\]
Percentage can be converted into fraction, by dividing the percentage by 100.
If the percentage is a%, then its fraction will be \[\dfrac{a}{100}\].
x% of a number y is given by \[\left( \dfrac{x}{100}\times y \right)\]
To convert decimal into percentage, it should be multiplied by 100.
To convert percentage into decimal, it should be divided by 100.
x% of y = y% of x
Now, on comparing the given values in the given question with the percentage formula we get,
\[x=20,y=2,40,000\]
Let us assume the amount he gained as G and the cost at which he purchased the plot as A.
\[\Rightarrow G=\dfrac{x}{100}\times y\]
Now, on substituting the corresponding values in the percentage formula we get,
\[\begin{align}
  & \Rightarrow G=\dfrac{20}{100}\times 2,40,000 \\
 & \Rightarrow G=20\times 2,400 \\
 & \therefore G=Rs48,000 \\
\end{align}\]
Now, the cost at which he purchased the plot will be the subtraction of the amount he gained from the amount at which he sold the plot.
\[\begin{align}
  & \Rightarrow A=2,40,000-G \\
 & \Rightarrow A=2,40,000-48,000 \\
 & \therefore A=Rs1,92,000 \\
\end{align}\]
Hence, he purchased the plot for Rs1,92,000.

Note: It is important to note that we need to subtract the amount of 20% of the amount at which he sold the plot from the total amount at which he sold the plot because it is given that he sold the plot by gaining some percentage of amount. That means he added some amount to the amount at which he purchased the plot and then sold it to someone.
Instead of assuming different variables for the percentage value he gained and the amount at which he purchased. We can directly assume some value at which he purchased the plot and then directly subtract 20% of 2,40,000 from 2,40,000 which takes less steps to solve. Both the methods give the same result.