Question

A person sells a table at a profit of 20%. If he had bought it at 10% less cost and sold for Rs. 105 more, he would have gained 35%. The cost price of the table is
(a) Rs. 7000
(b) Rs. 7350
(c) Rs. 9200
(d) Rs. 8140

Answer 1

Hint: Let the cost price of the table be ‘x’. Then, we calculate the selling price of the table at 20% profit in terms of ‘x’. We also calculate the cost price of the table at 10% less than actual price in terms of ‘x’. Now, we calculate the selling price of the table at 35% profit. Using all this given information we can easily find the cost price of the table.

Complete step-by-step answer:

Let, the cost price of the table be ‘x’.
Then, we calculate the selling price at 20% profit in terms of ‘x’:
S.P of the table at 20% profit\[=\dfrac{120}{100}\times Rs.x\]
S.P of the table at 20% profit$=Rs.\dfrac{6x}{5}$
C.P of the table when purchased at a price 10% less than actual price $=\dfrac{90}{100}\times Rs.x$
C.P of the table at 10% less than actual price is $Rs.\dfrac{9x}{10}$
Now, we calculate the selling price at 35% profit in terms of ‘x’ for purchase at 10% less:
S.P of the table at 35% profit$=\dfrac{135}{100}\times Rs.\dfrac{9x}{10}$ .
Then, according to the condition specified in the question:
$\begin{align}
  & \dfrac{6x}{5}+105=\dfrac{135}{100}\times \dfrac{9x}{10} \\
 & \Rightarrow \dfrac{6x}{5}+105=\dfrac{243}{200}x \\
 & \Rightarrow \dfrac{243}{200}x-\dfrac{6}{5}x=105 \\
 & \Rightarrow \left( \dfrac{243-240}{200} \right)x=105 \\
 & \Rightarrow x=\dfrac{105\times 200}{3}=Rs.7000 \\
\end{align}$
Hence, the cost price of the table is Rs.7000.
Therefore, the correct option is (a).

Note: The key step in solving this problem is the knowledge of profit or loss related to cost price and selling price of an article. If selling price is greater than cost price then profit occurs and if cost price is greater than selling price then loss occurs. This method is very useful for traders to survive in the market and analyze their business strategy.