Calculating Cost of Tax-Free Items in a Purchase

When you make a purchase that includes tax, it is not always immediately clear what portion of the total cost is due to the tax and what portion corresponds to the actual value of the item itself. This article will guide you through the process of calculating the cost of tax-free items given the total cost, the amount of tax paid, and the tax rate.

Understanding Sales Tax and Tax-Free Items

Sales tax is a tax that is added to the sale of goods and services. It is usually calculated as a percentage of the purchase price. In the context of this problem, you have made a purchase worth Rs. 45, out of which Rs. 30 went towards sales tax on taxable purchases. The tax rate for this purchase was 6%. To find the cost of the tax-free items, we need to subtract the cost of the taxable items from the total purchase.

Calculating the Cost of Tax-Free Items

Let's break down the problem step by step to find the cost of the tax-free items.

Step 1: Determine the Cost of Taxable Items

Given that the tax paid on the taxable items is Rs. 30, and the tax rate is 6%, we can set up the following equation:

Tax paid (Rs. 30) Tax rate (6%) × Cost of taxable items (X)

30 (6/100) × X

X 30 / (6/100)

X 30 × (100/6)

X 500/6

X 500 ÷ 6 ≈ 83.33 (This is actually the exact cost, so we should simplify further)

X 500/6 ≈ 5.00

Step 2: Calculate the Cost of Tax-Free Items

Now that we have determined the cost of the taxable items, we can find the cost of the tax-free items by subtracting the cost of the taxable items from the total purchase:

Cost of tax-free items Total purchase - Cost of taxable items

Cost of tax-free items Rs. 45 - Rs. 5.00

Cost of tax-free items Rs. 40.00

However, the problem statement states that the total is actually Rs. 25. Let's adjust our calculations to fit this information:

Taxed amount 6% of taxable items 30 paisa (0.30 Rs)

Let Y be the cost of taxable items.

0.06Y 0.30

Y 0.30 / 0.06 5.00 Rs

Therefore, the cost of taxable items 5.00 Rs

Cost of tax-free items Total purchase - Cost of taxable items

Cost of tax-free items 25 - 5.00

Cost of tax-free items 20 Rs

Conclusion

In this scenario, the cost of the tax-free items is Rs. 20 when the total purchase amount is Rs. 25 and the sales tax on taxable items is Rs. 30 (6% of the taxable purchase).

Additional Examples

Here are a few additional examples to reinforce the understanding:

Example 1: If the total purchase is Rs. 45, the sales tax paid is Rs. 30, and the sales tax rate is 6%, the taxable purchase amount can be calculated as:

Taxable purchase 30 / (6/100) 500/6 ≈ 5.00 Rs

Cost of tax-free items 45 - 5.00 40.00 Rs

Example 2: If the total purchase is Rs. 25, the sales tax paid is Rs. 0.30, and the sales tax rate is 6%, the taxable purchase amount can be calculated as:

Taxable purchase 0.30 / (6/100) 5.00 Rs

Cost of tax-free items 25 - 5 20 Rs

Example 3: If the total purchase is Rs. 25, the sales tax paid is Rs. 1.28, and the sales tax rate is 8%, the taxable purchase amount can be calculated as:

Taxable portion 1.28 / (8/100) 16 Rs

Taxed total 16 1.28 17.28 Rs

Cost of tax-free items 25 - 17.28 7.72 Rs

Understanding these calculations can be crucial for personal finance management and also for businesses looking to accurately track and report their sales and tax payments.