Question

Three articles A, B, and C are bought for Rs. 4,000 each. Article A is sold at a loss of 15%, and article B is sold at a profit of 25%. If the average selling price of all the three articles is RS. 3,960; at what profit or loss percent is the article C sold?

Answer 1

Hint: It is a word problem related to the money exchange, and the only thing that you need to focus on for solving this problem is the percentage calculation.

Complete step-by-step answer:
Let the selling price of article C be x.
Given:
The buying price of articles A, B, and C = Rs. 4,000
The average selling price of the three articles = Rs. 3,960
We know; article A was sold at a loss of 15%.
Now, calculating the loss by selling article A in Rupees:
Using the formula: Profit/Loss = $\dfrac{\text{percent profit/ loss}}{\text{100}}\text{ }\!\!\times\!\!\text{ Buying price}$ .
We get:
$\text{Loss on article A= Rs}\text{. }\dfrac{15}{100}\times 4000$
$\Rightarrow \text{Loss on article A= Rs}\text{. 600}$
Therefore, the selling price of article A = $\text{buying price - loss = 4000-600=Rs}\text{. 3,400}$ .
Similarly,
We know; article B was sold at a profit of 25%.
Now, calculating the profit by selling article B in Rupees:
$\text{Profit on article B= Rs}\text{. }\dfrac{25}{100}\times 4000$
$\Rightarrow \text{profit on article A= Rs}\text{. 1,000}$
Therefore, the selling price of article B = $\text{buying price + profit = 4000 +1000=Rs}\text{. 5,000}$ .
We know; an average of n numbers = $\dfrac{\text{sum of all the numbers}}{n}$ .
Applying the above formula:
Average of selling price of all three articles = 3960
$\Rightarrow \dfrac{\text{sum of selling price of all three articles}}{\text{3}}$ = 3960
$\Rightarrow \dfrac{3400+5000+x}{\text{3}}$ = 3960
$\Rightarrow 8400+x$ = 3 $\times $ 3960
$\Rightarrow x$ = 11880 – 8400
$\Rightarrow x$ = Rs. 3,480
So, the selling price of article C is Rs. 3,480.
Percent loss in article C = $\dfrac{\text{buying price - selling price}}{\text{buying price}}\times 100$ .
$\Rightarrow $ Percent loss in article C = $\dfrac{4000-3480}{4000}\times 100$ .
$\Rightarrow $ Percent loss in article C = $\dfrac{52}{4}$ .
$\Rightarrow $ Percent loss in article C = $13%$ .
Therefore, article B was sold at a loss of 13%.

Note: Don’t get confused and take the percentages with respect to selling price while you solve, as you should be very clear that the percentage loss or profit are terms related to the actual pricing not to the price for which you crack the deal. The other way of thinking of this is selling price might vary from buyer to buyer depending on the bargain they put in, but the percentage should be defined from a fixed mark so that you can easily handle it. The reason that most products in the market have an MRP tag on it, making it easier for all the sellers to handle their margins.