Question

There were two articles and the sum of cost prices of these articles is Rs. 500. One of them was sold at a profit of 20% and another at a loss of 20%. Besides if the selling prices of both the articles were same. Find the amount of overall loss

Answer 1

cost price=500
profit and loss are same so
overall loss percentage 20×20/100=4%
4% of 500 = 20 then
amount of over all loss = 500-20 = 480

Answer 2

Given,

The cost price of two articles is $500$

One is sold at $20%$% profit

One is sold at $20$% loss

As we can see it is given in the question that the selling price of both articles is the same.

To find,

Amount of overall loss

Solution,

Let the cost price of one article be x Rs.

The cost price of the other article will be ($500 -$x) Rs.

SP of  $1$ article ×$x + \frac{20}{100}$ × $x$

$= \frac{120}{100} x$

$= \frac{6}{5} x$

SP of the second article = $(500 - x) - \frac{20}{100} (500 - x)$

$= (500 - x) - (100 - \frac{x}{5}$$)$

$= 500 - x + 100 + \frac{x}{5}$

$= 600 - x + \frac{x}{5}$

Since SP of both articles are equal

$\frac{6}{5} x = 600 - x + \frac{x}{5}$

$\frac{6}{5} x + x - \frac{x}{5}$ $= 600$

$\frac{6x + 5x - x}{5}$$= 600$

$\frac{10x}{5} = 600$

$2x = 600$

$x = 300$

CP of the first article is Rs.300

CP of the second article is $500-300 = 200$

Profit on the first article is $300$ ×$20%$%

=$60$ Rs.

Loss on the second article is $200$ ×$\frac{20}{100}$

$=40$ Rs.

Net loss $= 20$ Rs.

The overall net loss as calculated is Rs.$20$