Question

A woman sold $ 15 $ bed sheets for Rs. $ 15,000 $ . Hence gaining $ 5 $ bedsheet’s cost prices. The cost per sheet is _______

Answer 1

Hint: Profit can be expressed when the selling price is greater than the buying price. Here, we are given a selling price but not given the buying price. First assume the buying price of the bedsheet to be “x” rupees.

Complete step-by-step solution:
Given that: A woman sold $ 15 $ bed sheets for Rs. $ 15,000 $ .
Selling price of one bed sheet $ = \dfrac{{15000}}{{15}} $
Find the multiples of the term on the numerator of the above expression.
Selling price of one bed sheet $ = \dfrac{{15 \times 1000}}{{15}} $
Common factors from the numerator and the denominator cancels each other.
Selling price of one bed sheet $ = 1000 $ Rs. --- (A)
Now, let us assume the given unknown cost price of the bed sheet be “x”
Therefore, the cost price of $ 15 $ bedsheets $ = 15x $
Given that women gain price of five bedsheets $ = 5x $
Now, profit or gain can be expressed as the difference between the selling price and the cost price.
Gain $ = S.P. - C.P. $
Place the values in the above expression –
 $ \Rightarrow 5x = S.P. - 15x $
Make the required term the subject –
 $ \Rightarrow 20x = SP $
Selling price, $ SP = 15000 $ (given)
 $ \Rightarrow 20x = 15000 $
 $ \Rightarrow x = \dfrac{{15000}}{{20}} $
 $ \Rightarrow x = 750 $ Rs.

Hence, the cost of one or the single bed sheet is Rs. $ 750 $

Note: Always remember that the selling price is always greater than the buying price when it is profit and when it is lost, the buying price is greater than the selling price. When there is no difference between the selling price and the buying price then there is no profit no loss. Be good in multiples and division and find the factors and remember the common factors from the numerator and the denominator cancels each other.