Question

A man sells two articles for the same price for Rs. 640. He earns the 20% profit on the first and 10% profit on the second. Find the overall percent profit.
A. 14.78%
B. 14.08%
C. 14.28%
D. 14.58%

Answer 1

Hint: The concept of percentages, profit and loss will be used in this question. The percentage can be converted into fraction by simply dividing them by 100. The relationship between cost price(CP) and selling price(SP) is-
$\begin{align}
  &SP = CP + {\text{P}}\% \;of\;CP \\
  &SP = CP + \dfrac{{\text{P}}}{{100}} \times CP \\
  &SP = \left( {1 + \dfrac{{\text{P}}}{{100}}} \right) \times CP \\
\end{align} $

Complete step-by-step solution -
Let the two articles be A and B. The selling price of both the articles is the same, that is, Rs. 640. We will find the total cost price and selling price for both the articles and then find the overall profit.
For article A we can write that,
$\begin{align}
  &S{P_{\text{A}}} = Rs.640 \\
  &\text{Applying the formula} - \\
  &S{P_{\text{A}}} = \left( {1 + \dfrac{{{{\text{P}}_{\text{A}}}}}{{100}}} \right)C{P_{\text{A}}} \\
  &640 = \left( {1 + \dfrac{{20}}{{100}}} \right)C{P_{\text{A}}} \\
  &640 = \dfrac{{120}}{{100}}C{P_{\text{A}}} \\
  &C{P_{\text{A}}} = Rs.533.33 \\
\end{align} $
For article B we can write that,
$\begin{align}
  &S{P_{\text{B}}} = Rs.640 \\
  &\text{Applying the formula} - \\
  &S{P_{\text{B}}} = \left( {1 + \dfrac{{{{\text{P}}_{\text{B}}}}}{{100}}} \right)C{P_{\text{B}}} \\
  &640 = \left( {1 + \dfrac{{10}}{{100}}} \right)C{P_{\text{B}}} \\
  &640 = \dfrac{{110}}{{100}}C{P_{\text{B}}} \\
  &C{P_{\text{B}}} = Rs.581.82 \\
\end{align} $
So, to find the total profit, we will find the total selling and cost prices. They can be calculated as-
$\begin{align}
  &C{P_{Total}} = C{P_{\text{A}}} + C{P_{\text{B}}} = 533.33 + 581.82 = Rs.1115.15 \\
  &S{P_{Total}} = S{P_{\text{A}}} + S{P_{\text{B}}} = 640 + 640 = Rs.1280 \\
    \\
\end{align} $
To find the net profit we will apply the formula as-
$\begin{align}
  &S{P_{Total}} = \left( {1 + \dfrac{{{{\text{P}}_{net}}}}{{100}}} \right)C{P_{Total}} \\
  &1280 = \left( {1 + \dfrac{{{{\text{P}}_{net}}}}{{100}}} \right)1115.15 \\
  &\dfrac{{{{\text{P}}_{net}}}}{{100}} = \dfrac{{1280}}{{1115.15}} - 1 = 1.1478 - 1 = 0.1478 \\
  &{{\text{P}}_{net}} = 14.78\% \\
\end{align} $
This is the required profit. The correct option is A.

Note: The students may find it confusing to identify the difference between the net profit and individual profits. It may seem that the net profit should be the average of the two profits, that is 15%, but the answer is slightly less than that. This is because the cost price of the two quantities are different, so it brings a slight change in the answer. Also, students should always ensure that their calculations are correct and should recheck them once the question is done.