Q.A customer pays Rs 1,050, inclusive of sales tax at 5%, for an article. Find the sale price (before tax) and the tax amount.

The Rs 1,050 given is tax-inclusive, so the (1 + r/100) factor must be divided out first.

Sale price = Rs 1,050 ÷ 1.05 = Rs 1,000. Tax = Rs 1,050 − Rs 1,000 = Rs 50.

Let the sale price before tax be P. Since r = 5%, 1.05P = 1,050, so P = 1,050 ÷ 1.05 = Rs 1,000.

Sales tax = 1,050 − 1,000 = Rs 50.

Check: 1,000 × 5% = 50, and 1,000 + 50 = 1,050 — matches the given figure.

Alternative — unitary method: Rs 1,050 represents 105 parts, so 1 part = 10, giving the sale price (100 parts) = Rs 1,000 and the tax (5 parts) = Rs 50.

Taking 5% of the given Rs 1,050 directly (giving Rs 52.50) instead of first recovering the sale price before tax is the standard trap in every tax-inclusive-to-exclusive problem — always divide out the tax factor first.