Calculating the Marked Price of a Washing Machine: A Comprehensive Guide

As a professional SEOer, it is essential to understand how to solve complex problems related to sales, gains, and marked prices. One such problem involves calculating the marked price of a washing machine when given the purchase price, discount, and profit percentage. This guide will walk you through a detailed step-by-step process using a real-world example.

Problem Statement

A dealer purchased a washing machine for Rs. 7660. After allowing a discount of 12% on its marked price, the dealer still gains 10% on the sale. The question is: what is the marked price of the washing machine?

Step-by-Step Solution

Step 1: Define Variables

Let the marked price of the washing machine be denoted as x.

Step 2: Calculate the Selling Price

The dealer allows a discount of 12% on the marked price, which means the selling price S is:

S x - 0.12 × x

Simplifying this, we get:

S 0.88x

Step 3: Determine the Gain

The dealer makes a 10% profit on the sale, and his purchase price is Rs. 7660. The gain can be calculated as:

Gain Selling price - Purchase price

10% of 7660 S - 7660

Therefore,

0.10 × 7660 0.88x - 7660

766 0.88x - 7660

7660 766 0.88x

8426 0.88x

x 8426 ÷ 0.88

x 9575

Therefore, the marked price of the washing machine is Rs. 9575.

Alternative Methods

Method 1: Using Gain and Selling Price

Alternatively, we can use the gain to find the selling price and then the marked price:

Gain 7660 × 10% Rs. 766

Selling price 7660 766 Rs. 8426

Given that the selling price is after a 12% discount on the marked price, the marked price can be calculated as:

Marked price 8426 / (1 - 0.12) 8426 / 0.88 Rs. 9575

Method 2: Using Direct Formula

We can also use a direct formula to find the marked price:

Marked price 7660 × 1.10 ÷ 0.88 9575

This method directly utilizes the gain and the discount to determine the marked price.

Conclusion

Understanding and solving such problems is crucial for any sales professional or entrepreneur. By mastering the calculations, one can effectively manage their inventory and improve their profit margins. The key steps involve determining the selling price via discount and then using the gain percentage to find the marked price.

For more resources on sales, gains, and pricing strategies, visit our website or contact us for professional consultation.