Question

A man sells a sofa set at a gain of 5%. If he had sold it for Rs. 490 less, he would have had a loss percentage of 2%. Find the cost price of the sofa set.
A. Rs. 7000
B. Rs 7200
C. Rs 6000
D. Rs 6500

Answer 1

Hint: Assume the value of cost price to be x. Then understand that you have been given the difference in selling price when it is sold in profit and when it sold in loss. Now by using the formula of Selling Price calculate the S.P. when the sofa set is sold in loss and when it is sold in profit. Find the difference and equate it to the value given in the question.

Complete step-by-step answer:

Let the cost price of the sofa set be x Rs.
According to question the gain on sofa set = 5%
And loss on sofa set = 2%
We know that S.P. for profit = \[\dfrac{{(100 + Profit\% )\operatorname{C} .P.}}{{100}}\]
And S.P. of loss = \[\dfrac{{(100 - loss\% )\operatorname{C} .P.}}{{100}}\]
So S.P. for profit = $\dfrac{{(100 + 5) \times x}}{{100}} = Rs.\dfrac{{21}}{{20}}x$
Now S.P. for loss = $\dfrac{{(100 - 2) \times x}}{{100}} = Rs.\dfrac{{49}}{{50}}x$
The difference between two S.P. ‘s is given in the question to be 490 Rs.
S.P. for profit – S.P. for loss = 490 Rs.
$(\dfrac{{21}}{{20}}x - \dfrac{{49}}{{50}}x) = (\dfrac{{105 - 98}}{{100}})x = Rs.\dfrac{7}{{100}}x$
$\dfrac{7}{{100}}x = 490$
$x = \dfrac{{490 \times 100}}{7} = Rs.7000$
Hence the correct answer is option A


Note: The principle of profit and loss is used in mathematics to determine the selling price of a product and to explain how profitable an enterprise is. Every product has a price for cost and selling price. We may measure the benefit earned or the loss suffered for a particular commodity on the basis of the values of those costs.