Question

After allowing $10\% $ of the marked price, the shopkeeper will get a profit of $25\% $ if the cost price of an article is rupees $180$ then Find its Marked Price.

Answer 1

Hint: In this scenario, to be measured one by one step, there may be some discount on this price and the actual selling price of the product may be less than the Marked price. then the products are sold to analyze a profit and loss definition and also given the discount of the item. It is helpful to measure the marked price to find the sale price from the provided data.

Formula Used:
When Discount is offered, ${\text{M}}{\text{.P > S}}{\text{.P}}$
When Discount is not offered, ${\text{M}}{\text{.P < S}}{\text{.P}}$
Where,
${\text{M}}{\text{.P}}$ is Marked Price,${\text{S}}{\text{.P}}$ is Selling Price
${\text{profit = S}}{\text{.P - C}}{\text{.P}}$
${\text{loss = C}}{\text{.P - S}}{\text{.P}}$
Where, ${\text{C}}{\text{.P}}$ is Cost Price
In case of Profit,
$S.P = C.P \times \dfrac{{100 + P}}{P}$
$C.P = \dfrac{{100 \times S.P}}{{100 + P}}$
Where, $P$ is Profit
In case of Loss,
$S.P = C.P \times \dfrac{{100 - L}}{{100}}$
$C.P = \dfrac{{100 \times S.P}}{{100 - L}}$
Where, $L$ is Loss

Complete step-by-step answer:
Given by,
Cost price $ = 180$
Profit$ = 25\% $
Also given that,
Discount$ = 10\% $
According to the Question:
 To find the Selling Price,
$S.P = C.P \times \dfrac{{100 + P}}{P}$
By using this formula,
We get,
$S.P = 180 \times \dfrac{{100 + 25}}{{100}}$
The above equation is simplified,
Here,
\[S.P = 225\]
Let as find Marked price,
${\text{Marked}}\,{\text{price}}\,{\text{ = }}\dfrac{{{{100 \times S}}{\text{.P}}}}{{{\text{100 - Discount}}}}$
We know that the value of $S.P$ and \[{\text{Discount}}\],
Substituting a above formula,
We get,
\[{\text{Marked}}\,{\text{price}} = \dfrac{{100 \times 225}}{{100 - 10}}\]
Simplified above equation is given by,
\[{\text{Marked}}\,{\text{price}} = 225 \times \dfrac{{100}}{{90}}\]
Solving the given equation,
We get,
\[{\text{Marked}}\,{\text{price}} = 250\]
So, the Marked Price will be \[Rs.250\].

Note: The above problem is defined as the price of the article we are using several formulas to find the solution. In this case the problem is based on profit and we know that the profit or loss formula to be substituted and to help this type of scenario extract the solution from the specific formula.