Q.The price of a television set, inclusive of sales tax at 12%, is Rs 22,400. Find the sale price (the price before tax) of the television set and the amount of sales tax included in it.

Since the tax-inclusive price is given, the formula must be reversed to recover the sale price before tax.

Sale price = Rs 22,400 ÷ 1.12 = Rs 20,000. Tax = Rs 22,400 − Rs 20,000 = Rs 2,400.

Let the sale price before tax be P. Since the tax rate is 12%, the tax-inclusive price is P × (1 + 12/100) = 1.12P.

Given 1.12P = 22,400, so P = 22,400 ÷ 1.12 = Rs 20,000.

Sales tax = 22,400 − 20,000 = Rs 2,400.

Check: 20,000 × 12/100 = 2,400, and 20,000 + 2,400 = 22,400 — both match the given figures exactly.

Alternative — unitary method: the inclusive price represents 112 parts out of 100 of the sale price, so 1 part = 22,400 ÷ 112 = 200, giving the sale price (100 parts) = Rs 20,000 and the tax (12 parts) = Rs 2,400.

A very common error is computing 12% of the given (tax-inclusive) figure Rs 22,400 directly, wrongly getting Rs 2,688 — this treats the inclusive price as if it were the pre-tax sale price, which it is not. Always divide out the (1 + r/100) factor first to recover the true sale price before computing the tax on it.