Question

100 oranges are bought for Rs.350 and sold at Rs.48 per dozen. The percentage of profit or loss is
A. $15\% {\text{ loss}}$
B. $15\% {\text{ gain}}$
C. $14\dfrac{2}{7}\% {\text{ }}loss$
D. $14\dfrac{2}{7}\% {\text{ profit}}$

Answer 1

Hint: The key observation in this question is the oranges are sold in dozens and since $1dozen = 12$, the total selling price can be calculated and hence the profit and %profit can be calculated using the formula $\% profit = \dfrac{{profit}}{{total{\text{ cost price}}}} \times 100$, where \[s.p = total{\text{ }}selling{\text{ }}price\].

Complete step-by-step answer:
Given,
\[Cost{\text{ }}price = Rs350\]
$Sell\operatorname{i} ng{\text{ price = Rs48 per dozen}}$
$Amount{\text{ of oranges = 100}}$
$ 1dozen = 12$
$Amount{\text{ of oranges in dozen = }}\dfrac{{{\text{100}}}}{{12}}$
$\therefore Total{\text{ }}Sell\operatorname{i} ng{\text{ price = Rs48}} \times \dfrac{{100}}{{12}}$
On simplifying further,
$\therefore Total{\text{ }}Sell\operatorname{i} ng{\text{ price = Rs400}}$
$ {\text{ selling price > cost price}}$
$\therefore profit = total{\text{ selling price}} - {\text{total}}\;{\text{cost price}}$
$ \Rightarrow profit = Rs\left( {400 - 350} \right)$
$ \Rightarrow profit = Rs50$
$ \% profit = \dfrac{{profit}}{{total{\text{ cost price}}}} \times 100$
\[ \Rightarrow \% profit = \dfrac{{50}}{{350}} \times 100\]
On simplifying further,
\[\% profit = \dfrac{{100}}{7}\]
The options are in mixed-fraction,
$\therefore $ The simple fraction $\dfrac{{100}}{7}$ can also be written in mixed fraction
The mixed-fraction form of $\dfrac{{100}}{7}$ is $14\dfrac{2}{7}$
\[ \Rightarrow \% profit = 14\dfrac{2}{7}\]
So, the correct answer is “Option D”.

Note: Profit margin, net margin, net profit margin or net profit ratio is a measure of profitability. It is calculated by finding the net profit as a percentage of the revenue.Profit margin is calculated with selling price (or revenue) taken as base times 100. It is the percentage of selling price that is turned into profit, whereas "profit percentage" or "markup" is the percentage of cost price that one gets as profit on top of cost price.