Question

On selling a table for Rs.987, Ron loses 6%. For how much did he purchase it?\[\]
A.Rs. 1050\[\]
B.Rs.1256\[\]
C.Rs.1350\[\]
D.Rs.1354\[\]

Answer 1

Hint: We recall the definitions cost price, selling price, loss and percentage loss. We use the formula $\%\text{Loss}=\dfrac{\text{CP}-\text{SP}}{\text{CP}}\times 100$ to find the cost price in rupees where \%Loss is the percentage loss SP is the cost price and SP is the selling price. \[\]

Complete step by step answer:
We know that cost price abbreviated as CP of an article is the price at which is the article is bought or the price that was spent for making the article from materials plus additional expenditure. The additional expenditure may taxes, transportation etc.\[\]
The selling price abbreviated as SP is the price at which the article is sold. If selling price is less than cost price then we say the sellers has caused loss. The gain amount is given by
\[\text{Loss}=\text{CP}-\text{SP}\]
The percentage gain is calculated on cost price as
\[\%\text{Loss}=\dfrac{\text{Loss}}{\text{CP}}\times 100=\dfrac{\text{CP}-\text{SP}}{\text{CP}}\times 100\]
We are given in the question that on selling a table for Rs.987, Ron loses 6%.So the selling price of Ron is $\text{SP}=\text{Rs}.987$ and the percentage loss is $\%\text{Loss}=6$. We put these given values in the formula for percentage loss to have,
\[\begin{align}
  & \%\text{Loss}=\dfrac{\text{CP}-\text{SP}}{\text{CP}}\times 100 \\
 & \Rightarrow 6=\dfrac{CP-987}{CP}\times 100 \\
\end{align}\]
We cross multiply to have,
\[\begin{align}
  & \Rightarrow 6CP=100\left( CP-987 \right) \\
 & \Rightarrow 6CP=100CP-98700 \\
 & \Rightarrow 100CP-6CP=98700 \\
 & \Rightarrow 94CP=98700 \\
 & \Rightarrow CP=\dfrac{98700}{94}=1050 \\
\end{align}\]

So, the correct answer is “Option A”.

Note: We note that if the selling price is greater than cost price the seller will earn grain or profit and percentage gain is given by $\%\text{Gain}=\dfrac{\text{Gain}}{\text{CP}}\times 100=\dfrac{\text{SP}-\text{CP}}{\text{CP}}\times 100$. We must be careful that both percentage gain and loss are calculated on cost price not selling price if not mentioned otherwise. We can alternatively assume $CP=x$ and solve the equation for $x$ in $x-\dfrac{\%\text{Loss}}{100}\times x=987$. We can directly find the cost price $CP=\dfrac{100}{100-\%\text{Loss}}\times SP$