Question

The difference between the cost price and sale price of an article is Rs 240. If the profit is 20%, the selling price is:
a. Rs 1440
b. Rs 1400
c. Rs 1600
d. None of these

Answer 1

Hint: In this problem, you must remember the concept of profit and loss.
Profit = Selling price(SP) - Cost price(CP) and $%\Profit=\dfrac{SP-CP}{CP}\times 100$
Similarly
Loss = Cost price(CP) - Selling price(SP) and $%Loss=\dfrac{CP-SP}{CP}\times 100$

Complete step-by-step answer:

Let the cost price of an article = Rs .CP
Let the selling price of an article = Rs. SP
According to question
$|SP-CP|=240$
We are using modulus here because we don’t know which one is greater, the cost price of an article, or the selling price of an article. But in the second line of question, it is given that the person is earning profit. So, in that case, SP is always greater than CP
Now, the difference in the cost price and selling price must be positive (i.e Rs 240).
So,
SP – CP = 240 ……….(1)
%Profit = 20% ---(given)---(2)
According to formula, we know that
$%\Profit=\dfrac{SP-CP}{CP}\times 100$

using (2)
$\begin{align}
  & \Rightarrow 20=\dfrac{SP-CP}{CP}\times 100 \\
 & \Rightarrow \dfrac{SP-CP}{CP}=\dfrac{20}{100} \\
 & using-(1) \\
 & \Rightarrow \dfrac{240}{CP}=\dfrac{1}{5} \\
 & \\
\end{align}$
Now, using cross multiplication, we get

$\begin{align}
  & \Rightarrow CP=240\times 5 \\
 & \Rightarrow CP=1200 \\
\end{align}$

Now using equation (1), we get

$\begin{align}
  & \Rightarrow SP-CP=240--(given) \\
 & \Rightarrow SP-1200=240--(CP=Rs.1200) \\
 & \Rightarrow SP=1200+240 \\
 & \Rightarrow SP=1440 \\
\end{align}$
Hence the selling price of the article is Rs.1440
Hence the correct option for this question is option (a)

Note: While solving this question, one can make a mistake by taking a simple difference between cost price and selling price (i.e CP – SP = 240), which is incorrect. To avoid such a mistake, we need to remember that the difference between the cost price of an article and the selling price of an article is positive and that is equal to Rs.240. Therefore we must use the modulus function. Because initially, we don’t know that which one is greater either cost price or selling price of an article