2.2 Profit, Loss, and Their Percentages

Figure: Profit and loss are always measured as a percentage of the Cost Price.

If SP > CP, the seller makes a profit (gain): > Profit = SP − CP

If SP < CP, the seller incurs a loss: > Loss = CP − SP

Profit or Loss percentage is always calculated on Cost Price, unless a question explicitly states otherwise (a classic examiner trap — watch for the phrase “on selling price,” which does occasionally appear in SSC questions and completely changes the answer).

Profit% = (Profit / CP) × 100 = [(SP − CP) / CP] × 100 Loss% = (Loss / CP) × 100 = [(CP − SP) / CP] × 100

Worked Example 1: A shopkeeper bought a fan for Rs 450 and sold it for Rs 540. Find his profit percentage.

Solution: Profit = 540 − 450 = 90. Profit% = (90/450) × 100 = 20%.

Worked Example 2: Ravi purchased a mobile cover for Rs 800 and sold it for Rs 680. Find his loss percentage.

Solution: Loss = 800 − 680 = 120. Loss% = (120/800) × 100 = 15%.

Worked Example 3: An article bought for Rs 1200 is sold for Rs 1500. Find the profit percentage.

Solution: Profit = 1500 − 1200 = 300. Profit% = (300/1200) × 100 = 25%.

A special case worth naming explicitly: when SP = CP, there is neither profit nor loss — this is called the break-even point, and profit%/loss% is simply 0%. You will see this phrase (“neither gains nor loses”, “no profit no loss”) repeatedly in word problems, and it always translates mathematically to SP = CP for that transaction (or, for a combined transaction involving multiple items, Total SP = Total CP).

It is also worth noting that profit and loss, unlike percentage change in general, are not symmetric. A 20% profit followed by a 20% loss on the resulting price does not bring you back to the original CP — this is really the same “successive percentage change” idea from the previous chapter, and it resurfaces constantly in Profit and Loss in the form of successive markups and discounts (Sections 2.5 and 2.7 below).

Worked Example 3A: A trader bought an old scooter for Rs 1350 and, after minor repairs, sold it for Rs 1215. Find his loss percentage.

Solution: Loss = 1350 − 1215 = 135. Loss% = (135/1350) × 100 = 10%.

Worked Example 3B: An article purchased for Rs 475 is sold for Rs 589. Find the profit percentage.

Solution: Profit = 589 − 475 = 114. Profit% = (114/475) × 100 = 24%. (Cross-check: 475 × 1.24 = 589 ✓.) These two examples are deliberately chosen so the resulting percentages — 10% and 24% — are not among the round numbers (15%, 20%, 25%) used in Worked Examples 1–3, so you get practice recognising that CP/SP problems do not always resolve to the “textbook” percentages.