Question

Two articles are sold for the same price such that a profit of 15% is made on one, and a loss of 15% is made on the other. Find the gain or loss percent on the whole.
(a) 2.25% loss
(b) 2.25% gain
(c) 5% loss
(d) 5% gain

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. Finally, after finding the net loss or gain, find its percentage with respect to the total selling price of the two combined.

Complete step-by-step answer:

To start with the solution, we let the cost price of the first article be x, and the cost price of the other article be y.

Profit in article one = 15% of its cost price = $\dfrac{15}{100}\times x$

Profit in the second article = 15% of its cost price = $\dfrac{15}{100}\times y$


Now the question states that the first article was sold for a profit of 15%. So, writing it in the form of an equation, we get

$\text{selling price of first article = cost price + profit = }x\text{+}\dfrac{15}{100}\times x$

The question also says that the second article was sold for a loss of 15%. So, we can represent this mathematically as:

$\text{selling price of second article= cost price - loss = }y-\dfrac{15}{100}\times y$

Now according to the question, the selling price of both the articles is equal. So, using the above two results, we can say:

$x+\dfrac{15}{100}\times x=y-\dfrac{15}{100}\times y$

Solving the above equation to find x in terms of y, we get

$\dfrac{100+15}{100}\times x=\dfrac{100-15}{100}\times y$

$\Rightarrow x=\dfrac{85}{115}\times y..........(i)$

Now, as asked in the question % profit is given by:

$\dfrac{\text{profit in article one - loss in the second article}}{\text{total selling price of both

article}}\times 100$

$=\dfrac{\dfrac{15x}{100}-\dfrac{15y}{100}}{x+y}\times 100$

$=\dfrac{15(x-y)}{x+y}$

Now substituting x from equation (i), we get

$=\dfrac{15\left( \dfrac{85}{115}- \right)}{\dfrac{85}{115}+}$

For simplifying the expression, we take 115 as the LCM from both numerator and

denominator and cancel it. On doing so, we get

$=\dfrac{15\left( 85-115 \right)}{85+115}$

$=-\dfrac{15\times 3}{20}$

$=-\dfrac{3\times 3}{4}=-\dfrac{9}{4}=-2.25%$

Moreover, as the answer is negative, we can say that the two articles as a whole are sold for

a loss of 2.25%. Therefore, the answer is option (a).

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 that the 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. For example: most products in the market have an MRP tag on it, making it easier for all the sellers to handle their margins.