 QUESTION

# A shopkeeper sells an article at a loss of $12\dfrac{1}{2}%$. Had he sold it for Rs.51.80 more then he would have profit of 6%. He cost price of the article is (a) Rs.280(b) Rs.250(c) Rs.380(d) Rs.240

Hint: We can take the cost price and the selling price as CP and SP respectively. Then we can use the formulae of profit and loss and solve them to obtain the answer.

It is given that the shopkeeper sells the article at a loss of $12\dfrac{1}{2}%$.

Now, the formula for loss is given by

Percentage Loss=$\dfrac{CP-SP}{CP}\times 100$ . Here the loss percentage is given by 12.5%.

Therefore,

\begin{align} & 12.5=\dfrac{CP-SP}{CP}\times 100 \\ & \Rightarrow SP=CP-\dfrac{12.5}{100}\times CP..........(1.1) \\ \end{align}

The formula for profit is given by

Percentage Profit=$\dfrac{SP-CP}{CP}\times 100.....(1.2)$ .

If he had sold it at a price of Rs.51.80, the SP would be SP+51.80 more then he would have

earned a profit of 6%. Therefore, by equation (1.2), we obtain,

$\Rightarrow SP+51.80=CP+\dfrac{6}{100}\times CP$………………………… (1.2)

Now, subtracting equation 1.1 from equation 1.2, we get

$\Rightarrow SP+51.80-SP=CP+\dfrac{6}{100}\times CP-(CP-\dfrac{12.5}{100}\times CP)$

$\Rightarrow 51.80=(\dfrac{6}{100}+\dfrac{12.5}{100})\times CP$

$\Rightarrow CP=\dfrac{51.80}{18.5}\times 100$

$\Rightarrow CP=280$

Thus, we obtain the cost price CP of the article to be Rs.280.

Hence, the correct option to the question is (e).

Note: We should be careful while using the percentage loss and profit formulae as in profit percentage, the term in the numerator is SP-CP while in loss percentage the numerator has the term CP-SP.