# A tradesman sold an article at a loss of 20%. Had he sold it for Rs.100 more, he should have gained 5%. The cost price of the article wasA) Rs 360B) Rs 400C) Rs 425D) Rs 450

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Hint: This question is based on profit and loss concept. We may assume some variable as cost price. Then we will find the selling price based on two different cases one with loss and other with gain. Accordingly equations will be prepared and solved to get the result.

Let us suppose that the cost price is Rs. X.
Now, we will compute its loss which is 20% of x.
So, loss = $x \times \dfrac{{20}}{{100}} \\ = \dfrac{x}{5} \\$
Selling price will be,
Selling Price = Cost Price – loss
SP = $x - \dfrac{x}{5} \\ = \dfrac{{4x}}{5} \\$
According to the question, now we will take the new selling price Rs 100 more. Then we get,
New SP = $\dfrac{{4x}}{5} + 100$
Since profit on this new selling price will be 5%.
So, profit (which is 5% of the cost price) = $x \times \dfrac{5}{{100}} \\ = \dfrac{x}{{20}} \\$ …..(1)
On the other hand this profit should be, New selling price – cost price
=$\dfrac{{4x}}{5} + 100 - x$….(2)
Thus both equations will be compared as follows to get value of x,
$\dfrac{{4x}}{5} + 100 - x = \dfrac{x}{{20}}$
Now, we will solve the above linear equation in x systematically by applying simple algebraic rules.
$\dfrac{{4x}}{5} + 100 - x = \dfrac{x}{{20}} \\ \Rightarrow 16x + 2000 - 20x = x \\ \Rightarrow 5x = 2000 \\ \Rightarrow x = 400 \\$
Value of x is 400.
Cost price of the article is Rs. 400.
So, option B is correct.

Note: This problem is a popular kind of profit and loss problems. In such questions percentage calculations are very important. Based on the loss or gain constraints equations should be framed carefully. With careful computation using algebraic rules and transformations, we have to get a solution of the equation.
* When the Selling price is more than the Cost price, profit is seen. * When the Selling price is less than the Cost price, loss is seen.