Question

A shopkeeper allows a discount of 10% to his customers and still gains 20%. Find the marked price of an article which costs Rs.450 to the shopkeeper.

Answer 1

Hint: We will let the marked price of the article be Rs.x. From the discount given, we will calculate the selling price of the article. From the cost price given we will calculate the gain in rupees. Finally we the formula SP = profit + CP and then equate it to selling price calculated in terms of x.

Complete step by step answer:
Given: Cost price of article = Rs.450, Discount = 10% and gain =20%
Let the marked price of the article be Rs. x
We know that selling price is calculated as:
Selling price(SP) = marked price – discount.
Putting the values, we get:
SP = Rs. x – 10% of Rs. x = Rs( x - $\dfrac{{10}}{{100}} \times x$)= Rs.$\dfrac{{9x}}{{10}}$.
$\because $ Cost price of the article = Rs.450 and gain = 20%
$\therefore $ Gain in rupees = 20% of Rs.450 = Rs.($\dfrac{{20}}{{100}} \times 450$)= Rs.90
We know that selling price is calculated as:
SP = CP + profit = Rs.(450 + 90)=Rs.540
On equating the two selling prices, we get:
$\dfrac{{9x}}{{10}}$=540
$ \Rightarrow $ 9x= 5400
$ \Rightarrow x = \dfrac{{5400}}{9} = 600$

Therefore, the marked price of the article = Rs.600

Note: In this question, you should know how to calculate selling if marked price and discounts are given. It is given as SP = marked price + %discount of marked price. Selling price can also be calculated if the cost price of the article and gain is given. You should remember the basic formula for calculating selling price i.e. SP = CP + profit and SP = CP – Loss.