Question

A man sells a sofa at a gain of 5%. Had he sold it for Rs.490 less, he would have lost 2%. Find the cost price of the sofa.

Answer 1

Hint: The question is related to profit and loss. In the question we have the selling price and the percentage of loss and gain by selling the sofa. We have to let the cost price be x. use the formula related to cost price and selling price.

Complete step-by-step answer:
Let the cost price of the sofa is x
We know that the
Selling price of sofa = cost price of the sofa + profit
now solve the question according to the first given condition which is
A man sells a sofa at a gain of 5%
Now putting the values in the formula
$sp = x + x.\dfrac{5}{{100}}$
Solving the equation, we get
$sp = \dfrac{{21}}{{20}}x$
Second condition
Loss of 2%
$sp = x - x.\dfrac{2}{{100}}$
$sp = \dfrac{{49}}{{50}}x$
According to the question
Difference in two selling prices
$ = \dfrac{{21}}{{20}}x - \dfrac{{49}}{{50}}x$
$ = \dfrac{{105 - 98}}{{100}}x$
$ = Rs.\dfrac{7}{{100}}x$
The difference between two selling prices is 490
$\dfrac{7}{{100}}x = 490$
$x = \dfrac{{49000}}{7}$
Divide the numerator by denominator
$x = 7000$
So now we have the value of x = 7000

So, the cost price of the sofa is Rs.7000

Note: Students mostly make the mistake in the selling price they assume that 490 is the selling price while 490 is the difference between two selling prices of the same sofa.
If the C.P is more than the S.P then loss is seen. If the S.P is more than the C.P then profit is seen.