Question

When a woman sells $ 20 $ articles for Rs. $ 160, $ there is $ 40\% $ loss. How many articles should she sell for Rs. $ 240 $ in order to earn $ 20\% $ profit?

Answer 1

Hint: Let the number of articles to be sold for profit be equal to “P” and frame the mathematical expression using the given word statements considering the loss when the articles are sold at Rs. $ 160 $ and profit when sold at Rs. $ 240 $

Complete step-by-step answer:
Let us consider that the number of articles to be sold at Rs. $ 240 $ be equal to $ = P $
Considering the given data for the profit and loss and the selling price.
 $ \dfrac{{\dfrac{{160}}{{20}}}}{{60}} = \dfrac{{\dfrac{{240}}{P}}}{{120}} $
Numerator’s denominator goes to the denominator.
 $ \dfrac{{160}}{{20 \times 60}} = \dfrac{{240}}{{P \times 120}} $
Find the factors on the numerator and the denominator of both the sides of the equation.
 $ \dfrac{{20 \times 2 \times 4}}{{20 \times 15 \times 4}} = \dfrac{{120 \times 2}}{{P \times 120}} $
Common factors from the numerator and the denominator cancel each other. Therefore, remove from the numerator and the denominator on the left hand side of the equation and similarly remove from the numerator and the denominator of the right hand side of the equation.
Simplified form becomes-
 $ \dfrac{2}{{15}} = \dfrac{2}{P} $
Find the cross product of the above expression, where the numerator of one side is multiplied with the denominator of the opposite side and vice-versa.
 $ \Rightarrow 2p = 2 \times 15 $
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ \Rightarrow p = \dfrac{{2 \times 15}}{2} $
Simplify
 $ \Rightarrow P = 15 $ articles.
Hence, women should sell $ 15 $ articles to get profit of $ 20\% $
So, the correct answer is “15”.

Note: Be careful while framing the mathematical expression from the given data. Be good in multiples and finding the factors, remember multiples of the numbers at least till twenty for the efficient and the accurate solution.