Question

By selling an article for Rs 168, five percent profit is made. For what price should it be sold to gain 10%

Answer 1

Hint: From the given information we must find the cost price of the article. After finding the cost price we will make use of the cost price and find the selling price with a 10% profit.

Formula used: $ \Rightarrow \cos t\;price = \;\dfrac{{100\; \times \;selling\;price}}{{100 + profit\,percentage}}...........(1)$
To find the selling price,
$ \Rightarrow selling\;price = \;\cos t\;price + \cos t\;price\left( {\dfrac{{profit}}{{100}}} \right)$………………………………(2)

Complete step-by-step answer:
Given, the selling price of an article = Rs 168
Given, the gain on the article =5%
So, Cost price of article by using formula (1) provided in hint and substituting the values given above
$ \Rightarrow \cos t\;price = \dfrac{{100 \times 168}}{{100 + 5}}$
Now multiplying 100 with 168 and adding 100 with 5, we get
$ \Rightarrow \cos t\;price = \dfrac{{16800}}{{105}}$
Dividing 16800 by 105, we get
$ \Rightarrow \cos t\;price = \;160................(3)$
So, the cost price of an article is Rs. 160
Given, profit in case of second scenario = 10 %
So, selling price for an article in second scenario by using formula (2) and using the value in equation (3)
$ \Rightarrow selling\;price = \;160 + 160\left( {\dfrac{{10}}{{100}}} \right)$
We will divide 10 with 100 and multiply the answer with 60 to get,
$ \Rightarrow \cos t\;price = \;160 + 16$
Now adding 160 with 16, we get
$ \Rightarrow \cos t\;price = \;176...................(2)$

So, for 10% profit the selling price of the article must be Rs. 176.

Note: One can generate a profit only if Selling Price> Cost Price
One generates a loss when Selling Price < Cost Price.
Profit and loss percentage is always calculated on cost price, unless otherwise specified.
Cost price (CP) The price, which is paid to acquire a product, is called cost price. All the overhead expenses (transportation, taxes etc.) are also included in the cost price.
Selling price (SP) The sum of money, which is finally received for the product i.e. the price at which the product is finally disposed off is called the Selling price.