Question

The labelled price of a cupboard is Rs.6500. The shopkeeper sold it by giving 5% discount on the labelled price and earned a profit of 15%. What approximately is the cost price of the cupboard?
A. Rs.5000
B. Rs. 5370
C. Rs.5600
D. Rs.5800
E. Rs.6000

Answer 1

Hint: To find the cost price, we have to find the selling price first. Labelled price is also called marked price. So find the discount price and subtract it from the marked price to get the selling price. Profit is 15%. To find the cost price, we have to substitute profit, selling price in the below mentioned formula.

Formula used:
$Profit = \dfrac{{\left( {SP - CP} \right)}}{{CP}} \times 100$, where SP is the selling price and CP is the cost price.

Complete step by step solution:
We are given that the labelled price of a cupboard is Rs. 6500. A shopkeeper sells it at a discount of 5% and the profit he makes is 15%.
We have to find the cost price of the cupboard.
The labelled price (marked price) MP is Rs. 6500.
Discount is 5%. 5% of Rs. 6500 is $\dfrac{5}{{100}} \times 6500 = Rs.325$
This means the discount price D is Rs.325.
Selling Price SP is equal to $MP - D = 6500 - 325 = Rs.6175$
We have SP, profit. Now we have to find Cost price.
$Profit = \dfrac{{\left( {SP - CP} \right)}}{{CP}} \times 100$
$15 = \left( {\dfrac{{6175 - CP}}{{CP}}} \right) \times 100$
$ \Rightarrow \dfrac{{15}}{{100}} = \dfrac{{6175 - CP}}{{CP}}$
On cross multiplication, we get
$ \Rightarrow 15CP = \left( {6175 - CP} \right)100$
$ \Rightarrow 15CP = 617500 - 100CP$
$ \Rightarrow 15CP + 100CP = 115CP = 617500$
$ \Rightarrow CP = \dfrac{{617500}}{{115}} = Rs.5369.56 \approx Rs.5370$
 Therefore, the cost price of the cupboard is Rs. 5370.
So, the correct answer is “Option B”.

Note: Do not confuse marked price with selling price. The actual selling price is marked price minus discount price, when there is any discount. If there is no discount then the marked price is the actual selling price. The price of an item will be reduced after bargaining, price before bargaining is marked price and price after bargaining is selling price (bargaining can also be considered as discount here). If there is no bargaining allowed and the object is at a fixed price, then the marked price is the same as selling price.