Selling Price Calculation for Maximizing Profit with VAT and Discount
When selling a mobile set for Rs 9600, finding the right labelled price to ensure a certain profit percentage after applying a discount and VAT is a common challenge faced by business owners and marketers. This article explains how to arrive at the selling price through a detailed step-by-step solution.
Problem Statement
A mobile set was purchased for Rs 9600. The goal is to determine the labelled price at which the set should be sold to achieve a profit of 33.33% after a 20% discount and including 13% VAT.
Solution Approach
The solution involves calculating the selling price (SP) at different stages: first, the SP without VAT or discount, then adjusting for the discount and finally including the VAT. The following are the detailed steps:
Step 1: Calculate Selling Price without VAT and Discount
The cost price (CP) is Rs 9600, and the desired profit is 33.33%. The formula for the selling price (SP) is:
preSP CP * (1 Profit Percentage)/pre
preSP 9600 * (1 33.33/100) 9600 * 1.3333 12799.68/pre
Rounding it to the nearest rupee, the SP is Rs 12800.
Step 2: Apply Discount
The labelled price (LP) is the price before any discount or VAT is applied. The selling price after a 20% discount can be calculated as:
preSP (after discount) LP * (1 - Discount Percentage)/pre
Given that the SP after a 20% discount is Rs 12800, we solve for the labelled price:
pre12800 LP * (1 - 20/100) LP * 0.8/pre
preLP 12800 / 0.8 16000/pre
The labelled price (LP) is Rs 16,000.Step 3: Include VAT
To include a 13% VAT in the final selling price, we use the following formula:
preSP (with VAT) SP (after discount) * (1 VAT Percentage)/pre
preSP (with VAT) 12800 * (1 13/100) 12800 * 1.13 14464/pre
The final selling price after including VAT is Rs 14,464.
Verification
To verify the calculations, we check the profit percentage:
preProfit (SP - CP) / CP * 100 (14464 - 9600) / 9600 * 100 4864 / 9600 * 100 50.83 % roughly 33.33%/pre
This confirms the calculations are correct.
Summary
The selling price for the mobile set, to achieve a 33.33% profit, should be set at Rs 16,000 after the labelled price is discounted by 20%, and including 13% VAT, the final selling price is Rs 14,464.