Profit and Loss for CSAT: Percentages, Discounts and Dishonest Dealers

Profit and Loss is the CSAT topic that tests buying and selling: cost price (CP) is what you pay, selling price (SP) is what you receive, and the difference is your profit (gain) when SP exceeds CP or your loss when it does not. The non-negotiable rule of the whole chapter is that profit and loss percentages are always calculated on cost price, never on selling price. CSAT asks 1 to 2 questions yearly, and the setters recycle a small set of traps.

The six base formulae

Everything in this chapter is arithmetic on CP and SP. Overhead expenses such as repairs or transport are added to the purchase price to get the true CP before any percentage is computed.

Worked example 1. A trader buys a second-hand refrigerator for Rs 2,500, spends Rs 500 on repairs, and sells it for Rs 3,300. Gain or loss percent? True CP = 2500 + 500 = Rs 3,000. Gain = 3300 - 3000 = Rs 300. Gain % = 300 x 100/3000 = 10 percent. Forgetting to add the repair cost is the designed mistake.

Worked example 2. A trader buys two fans at Rs 1,200 each, sells one at a 5 percent loss and the other at a 10 percent profit. Net result? SPs = 1200 x 95/100 = Rs 1,140 and 1200 x 110/100 = Rs 1,320. Total CP = 2400, total SP = 2460. Net profit = Rs 60. Always combine totals before judging profit or loss.

The same-SP trap: equal and opposite rates always lose

Worked example 3. Sohan sells two goats at the same price, making 10 percent profit on one and 10 percent loss on the other. Net effect? The CPs are SP/1.1 and SP/0.9. Total CP = SP x (1/1.1 + 1/0.9) = SP x 2.0202, which exceeds 2 x SP, so there is a net loss. The shortcut: selling at the same price with +x% and -x% always gives a net loss of (x/10)^2 percent. Here (10/10)^2 = 1 percent loss (CSAT 2014). The trap option 'no profit no loss' catches everyone who eyeballs it.

Discounts: marked price is not cost price

Marked price (MP) is the tag price before discount; discount is always computed on MP, while profit is computed on CP. Successive discounts multiply: a 10 percent then 15 percent discount is not 25 percent, it is 1 - 0.9 x 0.85 = 23.5 percent.

Worked example 4. A shopkeeper allows a 10 percent discount on the marked price of Rs 770 and still makes a 10 percent gain. Cost price? SP = 770 x 90/100 = Rs 693. CP = 693 x 100/110 = Rs 630 (CSAT 2016). Two steps, two different bases: discount on MP, gain on CP.

Worked example 5. Successive discounts of 10, 12 and 15 percent equal a single discount of? 1 - 0.9 x 0.88 x 0.85 = 1 - 0.6732 = 32.68 percent. Compute the survival fractions and multiply; never add the percentages.

The dishonest dealer: profit hidden in the weights

A dealer who 'sells at cost price' but delivers short weight still profits, because he sells 1 kg worth of money for less than 1 kg of goods. Profit % = shortfall x 100 / quantity actually delivered.

Worked example 6. A shopkeeper professes to sell at cost price but weighs 900 g instead of 1 kg. Profit % = 100/900 x 100 = 11.11 percent. With 950 g: 50/950 = 5.26 percent.

Worked example 7. A milkman mixes water with milk and claims to sell at cost price. With a 20 percent profit, how much water goes into each litre of pure milk? He pays for 1 L and sells 1.2 L of mixture at the milk's price, so 0.2 L = 200 ml of water per litre of milk. But if the question asks for water in each litre he delivers (the mixture), a 25 percent profit means 1.25M = 1 L delivered gives M = 0.8 L milk, so 200 ml water per delivered litre. Read which litre the question means.

Worked example 8. What percent of water must be mixed with honey to gain 20 percent by selling the mixture at honey's cost price (CSAT 2024)? Selling 120 units' worth for the cost of 100 units means 20 units of water per 100 of honey: 20 percent.

Ratio-style and reverse questions

Worked example 9. If a car is bought and sold for Rs 3,00,000 at a 20 percent loss, what was the cost price (CSAT 2020)? SP = 80 percent of CP, so CP = 3,00,000 x 100/80 = Rs 3,75,000.

Worked example 10. If CP is 80 percent of SP, what is the profit percent? SP = CP/0.8 = 1.25 x CP, so profit = 25 percent. Convert the given relation into a multiplier and the percent follows.

Worked example 11. Three articles P, Q, R cost Rs 3,330 together. P costs 25 percent more than R, R costs 20 percent more than Q. Cost of P (CSAT 2024)? Let Q = x. Then R = 1.2x and P = 1.25 x 1.2x = 1.5x. Total 3.7x = 3330 gives x = 900, so P = Rs 1,350.

Worked example 12. Cost price of 24 articles equals the selling price of 16. Gain percent? 24 x CP = 16 x SP gives SP = 1.5 x CP, so gain = 50 percent. The pattern 'CP of a = SP of b' gives gain or loss of (a - b)/b x 100 percent, positive when a exceeds b.

Traps that cost marks

First, computing the percent on SP: a '33.33 percent profit on selling price' is really 50 percent on cost price (gain = SP/3, CP = 2SP/3, gain/CP = 1/2). Second, the equal-and-opposite same-SP sale always loses, never breaks even. Third, adding successive discounts instead of multiplying the survival fractions. Fourth, forgetting overheads in CP. Fifth, mixing the bases: discount on marked price, profit on cost price, dealer profit on quantity actually delivered.

Speed tips for the exam hall

Translate every percent into a multiplier instantly: +10 percent = 1.1x, -20 percent = 0.8x. For 'CP of a = SP of b' questions, the percent is (a - b)/b x 100. For two items sold at the same price with +x% and -x%, write (x/10)^2 percent loss without calculating. For successive discounts, multiply 0.9-style fractions. And always ask 'percent of what': the base is cost price unless the stem explicitly says otherwise.

Key Terms

• Cost price (CP) is the total price paid to acquire an article, including the purchase price plus overheads like repairs and transport. All profit and loss percentages are computed on CP.
• Selling price (SP) is the price at which an article is actually sold. Comparing SP with CP decides profit (SP > CP) or loss (SP < CP).
• Marked price (MP) is the tag or list price printed on an article before any discount. Discounts are always computed on MP, never on CP.
• Discount is a reduction offered on the marked price, so that SP = MP minus discount. Successive discounts apply one after another on the shrinking price.
• Overhead expenses are extra costs like repairs, transport or packing that are added to the purchase price to arrive at the true cost price.
• Gain percent / Loss percent are (SP - CP) x 100 / CP and (CP - SP) x 100 / CP respectively. The denominator is always cost price.