Profit, loss, discount, tax — which formula to use for word problems

Question

A shopkeeper buys a shirt for Rs 600 (cost price) and sells it for Rs 750. Find the profit and profit percentage. If the selling price included a 5% GST, what was the price before tax?

Solution — Step by Step

Profit $= SP - CP = 750 - 600 = \text{Rs } \mathbf{150}$

Profit % $= \frac{\text{Profit}}{CP} \times 100 = \frac{150}{600} \times 100 = \mathbf{25\%}$

Key point: profit/loss percentage is always calculated on cost price, not selling price.

If Rs 750 includes 5% GST, then $750 = \text{Price before tax} + 5\%$ of price before tax.

750 = P \times \left(1 + \frac{5}{100}\right) = 1.05P

P = \frac{750}{1.05} = \mathbf{\text{Rs } 714.29}

Why This Works

graph TD
    A["Word Problem Type?"] --> B["Buying and selling → Profit/Loss"]
    A --> C["MRP with reduction → Discount"]
    A --> D["Price with extra charge → Tax"]
    B --> E["Profit = SP - CP"]
    B --> F["Loss = CP - SP"]
    B --> G["Profit% = Profit/CP × 100"]
    C --> H["Discount = MRP - SP"]
    C --> I["Discount% = Discount/MRP × 100"]
    D --> J["Tax amount = Tax% × Price"]
    D --> K["Bill amount = Price + Tax"]

The core idea: profit/loss is always on cost price, discount is always on marked price (MRP), and tax is always on the selling price. These are three different reference points, and mixing them up is the number one source of errors.

When a problem combines all three (marked price, discount, then tax), the sequence is: MRP → apply discount → get SP → apply tax → get bill amount.

Alternative Method

For successive changes (like two successive discounts of 20% and 10%), do NOT add them. A 20% discount followed by 10% is NOT 30% total.

Instead, use the multiplier method: $\text{Final price} = \text{MRP} \times 0.80 \times 0.90 = \text{MRP} \times 0.72$ . So the effective discount is 28%, not 30%.

This multiplier approach works for any chain of percentage changes and is much faster than computing step by step.

Common Mistake

Calculating profit percentage on selling price instead of cost price. If CP = 600 and SP = 750, the profit is 150. Profit% = $150/600 \times 100 = 25\%$ (correct). Many students mistakenly write $150/750 \times 100 = 20\%$ (wrong — that is the profit as a percentage of SP, not CP). In CBSE, profit and loss percentages are always computed on cost price unless explicitly stated otherwise.