Calculating the Purchase Price of a Watch: A Comprehensive Guide
In this article, we will explore how to calculate the purchase price of a watch given certain selling price conditions. This involves understanding the relationship between the marked price, cost price, and the applied discounts.
Introduction
When dealing with price and profit adjustments, it's crucial to understand how much the shopkeeper initially paid for the item and how much they aim to profit from it. This article will provide a step-by-step process to determine the purchase price of a watch based on its marked price and the selling price after a discount.
Problem Definition
A watch was sold at its marked price with a gain of 20, but after allowing a 5 discount, the gain would have been Rs. 140 only. We need to find out at what price the shopkeeper purchased the watch.
Step-by-Step Solution
To solve this problem, let's define the following variables:
CP (Cost Price): The price at which the shopkeeper purchased the watch. MP (Marked Price): The price at which the watch is marked for sale.Step 1: Establish Equations Based on the Problem
First, we need to set up the equations based on the given information:
When the watch is sold at its marked price with a gain of 20, the selling price (SP) is: When a 5 discount is allowed on the marked price, the selling price is: After the discount, the selling price results in a gain of Rs. 140.The equations can be derived as:
Selling price at marked price (SP) with a gain of 20:
SP MP 1.20CP
Selling price after a 5 discount (SPdiscounted):
SPdiscounted MP - 0.05MP 0.95MP
Selling price with a gain of Rs. 140:
SPdiscounted CP 140
Step 2: Substitute and Solve
By substituting the first equation into the second, we get:
0.95MP CP 140
Revising MP as 1.20CP:
0.95(1.20CP) CP 140
Simplifying the equation:
1.14CP CP 140
Step 3: Rearrange and Solve for CP
Subtract CP from both sides:
1.14CP - CP 140
0.14CP 140
Solving for CP:
CP 140 / 0.14 1000
Conclusion
The shopkeeper purchased the watch for Rs. 1000.
Explanation of the Solution
The solution involves using the relationship between the marked price, cost price, and the applied discount. By solving the equations, we can determine the cost price and ensure the shopkeeper's profit margin is maintained appropriately.