Profit-Loss

One rule governs the whole chapter: profit and loss percentages are ALWAYS calculated on the cost price, while discount is ALWAYS calculated on the marked price. Draw the three prices as a line — cost price, then marked price above it, then selling price after the discount — and every question is just a walk along that line. When a shopkeeper marks up and then discounts, apply the two percentages to their own bases in order, never add or subtract them directly.

• Profit or loss percentage is always on cost price, never on selling price.

  '20% profit' means selling price is 120% of cost price — the base is always what was paid, not what was received. This is the same base-confusion trap that appears in percentage-change questions, wearing a shopkeeper's costume.

• Successive discounts multiply, they do not add.

  A '20% then 10%' discount is not a 30% discount. Apply each discount to what remains after the previous one — the effective discount is always slightly less than the simple sum.

• 1Selling price = Cost price x (1 + profit%/100) for a profit, or x (1 - loss%/100) for a loss.
• 2Marked price is the label price before any discount; selling price is marked price after the discount is applied.
• 3Two successive discounts of a% and b% together equal a single discount of (a + b - ab/100) per cent, not (a + b) per cent.
• 4If a trader claims to sell at cost price but uses a false weight, the effective profit percentage can be calculated from the shortfall in weight, independent of the stated price.

• Profit percent = (selling price - cost price) / cost price x 100. The base is the cost price, never the selling price.
• Discount percent = (marked price - selling price) / marked price x 100. The base here is the marked price.
• Selling price = cost price x (100 + profit percent)/100; for a loss, use (100 - loss percent)/100.
• Selling two articles at the same price, one at x% profit and the other at x% loss, always gives a net LOSS of (x squared)/100 percent.
• If a dealer uses false weights, profit percent = error / (true value - error) x 100, which is why selling 900 grams as a kilogram is not a 10% gain.

• Two successive discounts of 10% each do not equal a flat 20% discount — the combined effect is 19%, because the second discount applies to an already-reduced price.

• Quantitative Aptitude for Competitive Examinations — R S Aggarwal
• Fast Track Objective Arithmetic — Arihant
• NCERT Class VIII — Mathematics

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