CAT Quant · Study & Practice

Profit, Loss & Discount

AreaArithmetic DifficultyEasy–Moderate CAT weightage2–4 questions (directly + blended with Percentages, Ratio and DI)

Profit, Loss and Discount is percentages wearing a business suit. Every formula in this chapter is just a percentage taken on a base, and the only real skill CAT tests is knowing WHICH base each percentage sits on — cost price for profit and loss, marked price for discount. Get the base wrong and the whole problem collapses; get it right and most questions fall in two lines. The vocabulary is fixed: cost price (CP) is what the seller pays, selling price (SP) is what the buyer pays, marked price (MP) is the sticker before any discount, and the gap between MP and SP is the discount. CAT loves to layer these: a shopkeeper marks goods up, offers a discount, still profits, and may cheat on the weight as well. This chapter walks through the price relationships, the profit and loss multipliers, single and successive discounts, the equivalent-discount shortcut, the false-weights trick that quietly inflates margins, and partnership, where profit is split by capital and time. Throughout we favour the multiplier and assume-CP-is-100 methods over slow arithmetic, because in CAT the marks go to whoever sets up the base fastest and never confuses MP with CP.

Topics

1 Cost, Selling & Marked Price 4 worked · 5 practice · 8-Q test Start → 2 Profit & Loss % 4 worked · 5 practice · 8-Q test Start → 3 Discount & Successive Discount 4 worked · 5 practice · 8-Q test Start → 4 Equivalent Discount 4 worked · 5 practice · 8-Q test Start → 5 False Weights 4 worked · 5 practice · 8-Q test Start → 6 Partnership in Trade 4 worked · 5 practice · 8-Q test Start →

⚡ CAT shortcuts & speed methods

The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.

  • Lock the base: profit/loss is on CP, discount is on MP. Wrong base is the #1 error here.
  • Assume CP = ₹100. Then mark-up, discount and SP become clean numbers you read off in one pass.
  • Successive discounts d1, d2 → single = d1 + d2 − d1·d2/100 (cross term SUBTRACTED).
  • Same SP, one item +x% and one −x% → always a net LOSS of (x/10)² %, never break-even.
  • False weight sold at CP → gain = error/(true − error) × 100; the base is the actual weight given.
  • Partnership: split profit by (capital × time). Equal time ⇒ split is just the capital ratio.

⚠️ Common mistakes & traps

CAT is designed so that careless errors here cost you marks. Internalise each trap before the exam.

  • Taking profit % on the selling price instead of the cost price.
  • Adding successive discounts (20% + 25% ≠ 45%; the single equivalent is 44%).
  • Computing the false-weight gain on the claimed weight instead of the actual (smaller) weight.
  • Assuming "+x% then −x%" on equal SPs breaks even — it is always a (x/10)² % loss.
  • Forgetting to add overheads (transport, repairs) to the cost price before finding profit.

📈 CAT exam insight & PYQ analysis

CAT rarely poses a bare "find the profit %" anymore; profit-loss arrives fused with percentages, ratios and occasionally DI. The recurring high-value patterns are: successive/equivalent discount comparisons ("which offer is better"), the mark-up-then-discount chain that still nets a stated profit, the equal-SP gain-and-loss trap, and false-weight dishonest-dealer sums. Partnership shows up more in XAT, SNAP and NMAT than in recent CAT papers, usually with unequal investment periods. Difficulty stays Easy–Moderate, but speed matters: the assume-CP-100 and multiplier-chain methods convert two-minute algebra into ten-second mental work, which is where the percentile is won.

🎴 Flashcards — instant recall

Tap a card to reveal the answer. Drill these until they are automatic.

Profit % is taken on which price?Tap to reveal
Cost price (CP)
Discount % is taken on which price?Tap to reveal
Marked price (MP)
SP from CP at p% profit?Tap to reveal
SP = CP × (1 + p/100)
CP from SP at p% profit?Tap to reveal
CP = SP ÷ (1 + p/100)
Single discount equal to d1 then d2?Tap to reveal
d1 + d2 − d1·d2/100
Two successive 10% discounts = single?Tap to reveal
19%
Same SP, +x% and −x% net effect?Tap to reveal
Loss of (x/10)² %
False weight (at CP) gain formula?Tap to reveal
error/(true − error) × 100
Sell 900 g per claimed kg at CP ⇒ gain?Tap to reveal
11.11% (1/9)
Partnership profit split ratio?Tap to reveal
capital × time
Buy 12 for the price of 10 ⇒ profit %?Tap to reveal
20%
CP 100, marked +40%, 30% off ⇒ result?Tap to reveal
2% loss (SP = 98)

📌 Quick revision

Three prices drive everything: CP (seller’s cost), SP (buyer pays), MP (sticker). Fix the base — profit/loss on CP, discount on MP — and most sums fall in two lines. Use multipliers: SP = CP(1 ± rate/100), SP = MP(1 − d/100); reverse by dividing. Successive discounts combine as d1 + d2 − d1·d2/100, never the plain sum. Equal SPs at ±x% give a (x/10)² % loss. A false weight sold at cost gives gain = error/(true − error) × 100 on the actual weight. Partnership profit splits by capital × time. Assume CP = 100 to keep every number clean.

Chapter test

📝 Profit, Loss & Discount — Chapter Test
25 fresh questions · timed · full solutions
Start chapter test →
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🏆 Vidaara CAT success checklist

You have truly mastered Profit, Loss & Discount when you can tick every box below.

  • Recall every formula in this chapter without looking them up
  • Solve each topic’s practice set with at least 80% accuracy
  • Use the chapter shortcuts to cut your solving time in half
  • Spot and avoid every common trap listed above
  • Score 80%+ on the timed chapter test

📋 Chapter mastery scorecard

Track where you stand. Aim for the target before moving to the next chapter.

Skill checkpointTarget
Concept theory & formulas understood100%
Topic practice sets attempted (6 topics)6/6
Best topic-test score— → 80%+
Chapter test score— → 80%+
Flashcards drilled to instant recall12 cards