Question

A shopkeeper allows $ 15\% $ discount and still marks $ 5\% $ profit. Find the marked price of an article which costs him $ Rs.340 $ .
A) $ Rs.440 $
B) $ Rs.350 $
C) $ Rs.380 $
D) $ Rs.360 $

Answer 1

Hint: To solve this question, we will take the help of cost price and by applying the formula for the selling price and the marked price, we will be finding out the Marked price. Hence, with the given values and applying the formulas to them, we can solve this question.
Formula used-
Selling price= cost price + profit
Marked price = selling price+ discount
Now let’s solve the given question as follows-
It is given in the question that the Article costs \[340\] but the gains $ 5\% $ profit on it which makes the selling price.
So, given cost price= \[CP = Rs.340\],
Profit = $ 5\% $ of the cost price.
So, profit= $ 5\% \times 340 $
 $ \Rightarrow profit = \dfrac{5}{{100}} \times 340 $
 $ \Rightarrow profit = Rs.17 $
So Now applying the formula for the selling price,
Selling price= cost price + profit
 $ \Rightarrow SP = CP + profit $
 $ \Rightarrow SP = Rs.(340 + 17) $
 $ \Rightarrow SP = Rs.357 $

Complete step by step answer:
Now, when we talk about the marked price, it can be calculated by the addition of the discount provided by the seller to the selling price (that we have just calculated).
Let the marked price is $ x $ .
Then according to the question,
Discount= $ 15\% $ of the marked price.

 $ \Rightarrow Discount = 15\% \times (x) $
 $ \Rightarrow Discount = \dfrac{{15x}}{{100}} $
Also, from the formula for the marked price,
Marked price = selling price+ discount
 $ \Rightarrow x = SP + \left( {\dfrac{{15x}}{{100}}} \right) $
 $ \Rightarrow x = 357 + \left( {\dfrac{{15x}}{{100}}} \right) $
 $ \Rightarrow x - 0.15x = 357 $
 $ \Rightarrow 0.85x = 357 $
 $ \Rightarrow x = \dfrac{{357}}{{0.85}} $
 $ \Rightarrow x = 420 $
Hence the marked price of the article is $ Rs.420 $.
So, option (A) is the correct answer.

Note:
We should also know the meaning of the terms used in the question.
Marked price - Marked price is an MRP of an article that represents the maximum amount on which the shopkeeper can sell it.
Selling price - Selling price is defined as the price at which a good or service is sold by the seller to the buyer. It is generally demonstrated in currency units.
Discount – the term discount can be defined as a percentage or amount deducted from the normal selling price of a product. In simple words, it means reductions of price by a percentage or an amount.
Profit: Profit is the available income from producing an additional item. Profit is the auxiliary income gained from selling an additional well.
So, we came to the conclusion that,
The selling price is not equal to the Marked price.
Because the marked price is what’s printed on the article but the selling price is what’s settled between the two parties.