Finding the Cost Price of a Mobile Phone Using Discount and Loss

Introduction

Businesses often face situations where understanding the cost price of a product is crucial for making informed decisions. Here, we explore a scenario involving a mobile phone. Let's dive into the problem step by step and find the cost price using mathematical reasoning and calculations.

Problem Description

A shopkeeper sold a mobile phone for Rs. 12,000. Had he offered a 10% discount on the selling price, there would have been a loss of Rs. 4. Our goal is to find the cost price of the mobile phone.

Step-by-Step Solution

Step 1: Calculate the Selling Price After the 10% Discount

The discount on the selling price is:

10% of Rs. 12,000 0.10 times; 12,000 Rs. 1,200

Thus, the selling price after the discount (SP) is:

SP Rs. 12,000 - Rs. 1,200 Rs. 10,800

Step 2: Relate the Selling Price After Discount to the Cost Price

Since there is a loss of Rs. 4, the selling price after the discount (Rs. 10,800) represents 96% of the cost price (CP).

SP CP - Loss CP times; (1 - Loss Percentage) CP times; 0.96

Therefore, we can write:

Rs. 10,800 CP times; 0.96

Step 3: Set Up the Equation and Solve for Cost Price (CP)

Now, let's solve for the cost price (CP) by rearranging the equation:

CP Rs. 10,800 div; 0.96 Rs. 11,250

Conclusion

Therefore, the cost price of the mobile phone is Rs. 11,250.

Alternative Methods

Let's look at a few more ways to solve this problem using the same information provided:

Method 1: Direct Calculation

The discounted price would be:

Rs. 12,000 times; 90/100 Rs. 10,800

Rs. 10,800 is a loss of Rs. 4, meaning it represents 96% of the cost price (CP). Therefore,

CP Rs. 10,800 times; 100/96 Rs. 11,250

Method 2: Using Loss Percentage

Let 'x' represent the cost price (CP).

After a 10% discount, the selling price (SP) is: Rs. 12,000 times; 90/100 Rs. 10,800 Rs. 10,800 is 96% of the cost price (CP), so: CP Rs. 10,800 times; 100/96 Rs. 11,250

Method 3: Using the Loss Factor

The price without discount is:

Rs. 12,000 div; (1 - 0.10) Rs. 13,333.33

Cost price (CP) can be calculated using the loss factor:

CP (SP div; (1 - Loss Percentage)) times; (1 - Loss Percentage) / (1 - Loss Percentage) Rs. 13,333.33 div; 0.96 Rs. 13,888.89

Using a simplified method, we can also directly use:

CP Rs. 13,333.33 div; 0.96 Rs. 13,888.89

However, the most straightforward and commonly used solution is the first method, which gives us:

CP Rs. 11,250