Question

A man sold an article at a loss of 20%.lf he had sold it for Rs 50 more , he would have gained 5%. What is the CP of the article

Answer 1

Step-by-step explanation:

Let the cost price of the article be x.

According to the question, he sold the article at a loss of 20%.

Formula to calculate Selling price when loss% and Cost Price is given =

$\sf SP = \Bigg (\dfrac{100-Loss \%}{100} \Bigg )CP$

Using this formula,

$\sf SP = \Bigg (\dfrac{100-20}{100}\Bigg )x = \dfrac{80}{100}x = \dfrac{4}{5}x$

Selling price when for 5% gain on the article.

$\sf SP = \Bigg ( \dfrac{100+Profit \%}{100} \Bigg )CP$

Using this formula,

$\sf SP = \Bigg (\dfrac{100+5}{100} \Bigg )x= \dfrac{105}{100}x = \dfrac{21}{20}x$

Now we've been given that he sold the article at 20% loss. If he would've sold it for ₹50 more, he would've gained 5% on the article.

Therefore, we can conclude, that the difference between the selling price of the article at 20% loss and 5% gain will be ₹50.

$\sf \dfrac{21}{20}x - \dfrac{4}{5}x = 50$

$\sf \implies \dfrac{21- 16}{20}x = 50$

$\sf \implies \dfrac{5}{20}x = 50$

$\sf \implies \dfrac{1}{4}x = 50$

$\sf \implies x = 50 \times 4 = 200$

Therefore, the cost price of the article is ₹200.