Profit and Loss
~12 min read
- What: Profit and Loss covers cost price, selling price, marked price, profit/loss percent, successive discounts, and the standard CDS variants — false weights, dishonest dealers, and mixed-rate sales.
- Why it matters: CDS averages 3–4 questions per paper on this single chapter — pure percentage application with high yield per minute.
- Key fact: Profit % and Loss % are always computed on Cost Price (CP), never on Selling Price (SP). CDS plants this trap in nearly every paper — read the question carefully.
Profit and Loss is the most-tested commercial-arithmetic chapter in CDS. The formulas are tight and recognisably percentage-flavoured, but the trap density is high — sign errors, base errors (CP vs SP), and successive-discount slip-ups cost more marks here than any other arithmetic chapter.
This page is built from CDS Previous Year Questions across 2000–2023. Pair with Percentage (its conceptual parent) and Ratio and Proportion (alligation in dishonest-dealer problems).
What This Topic Covers
CDS scope: (1) basic definitions — CP, SP, MP, profit, loss; (2) profit/loss percent — always on CP; (3) discount — discount on MP; (4) successive discounts — net effect formula; (5) marked-price problems — relationship CP → MP → SP; (6) false weights / dishonest dealer — claimed vs actual quantities; and (7) mixed-rate sales — overall profit from items sold at different rates.
Why This Topic Matters
- 3–4 CDS questions per paper, with high pace requirement.
- Successive discount uses the same \(x + y + xy/100\) formula as successive percentages.
- False-weight problems are a CDS specialty that rewards crisp percentage reasoning.
Exam Pattern & Weightage
| Year / Paper | No. | Subtopics Tested |
|---|---|---|
| 2007-I/II | 3 | Profit %, two-article comparison |
| 2009-II | 2 | Successive discount, marked price |
| 2010-I/II | 4 | Discount, false weight, profit % |
| 2011-I/II | 3 | Mixed rate, marked-price puzzle |
| 2012-I/II | 3 | Dishonest dealer, successive discount |
| 2014-I/II | 3 | Profit % on SP vs CP, discount |
| 2016-I/II | 3 | Mixed sale, equal SP both profit/loss |
| 2017-I/II | 3 | Marked price problems, successive discount |
| 2018-I/II | 3 | Discount, mixture |
| 2019-II | 2 | False weight, profit % |
| 2020-I/II | 3 | Successive discount, mixed rate |
| 2021-I/II | 3 | Marked price, discount with profit |
| 2023-I | 2 | Mixed application |
"Two articles sold at the same SP, one at \(x\%\) profit and one at \(x\%\) loss — what is the overall profit/loss?" Always a loss. Specifically, \(\text{loss}\% = (x/10)^2\). At 10% each, loss is 1%; at 20% each, loss is 4%. CDS recycles this every other paper.
Core Concepts
Basic Definitions and Identities
Profit/loss percent is always on CP. If a CDS option offers "profit percent on selling price", it is a distractor — convert to CP-basis before answering.
Marked Price and Discount
The marked price (MP) is the labelled price. Discount is a reduction from MP. The selling price (SP) after discount is:
Successive Discounts
Note the minus sign: discounts apply to a shrinking base, so the combined effect is less than the sum.
Two SPs Equal, One Profit One Loss
Where \(x\%\) is the profit on one article and loss on the other. Always a net loss.
False Weights / Dishonest Dealer
Dealer claims to sell at cost price, but uses a weight that is short. If actual weight is \(W\) but claims \(W'\) (where \(W' > W\)):
Example: claims to sell 1000 g but gives 900 g — profit \(= 100/900 \times 100 = 11.11\%\).
Worked Examples
Example 1 — Profit % (2007-I)
Q: An article is bought for ₹450 and sold for ₹540. Find the profit percent.
- Profit \(= 540 - 450 = 90\). Profit% \(= 90/450 \times 100 = 20\%\).
Example 2 — Successive Discount (2009-II)
Q: A shopkeeper offers successive discounts of 20% and 10% on the marked price. What is the single equivalent discount?
- Apply: \(d_1 + d_2 - d_1 d_2 / 100 = 20 + 10 - 200/100 = 28\%\).
Example 3 — Equal SP, One Profit One Loss (2016-II)
Q: Two pens are sold at the same price. One at 20% profit, the other at 20% loss. What is the net result?
- Apply: overall loss% \(= (20/10)^2 = 4\%\).
- The dealer makes a 4% net loss.
Example 4 — False Weight (2019-II)
Q: A grocer sells goods at cost price but uses a 950 g weight in place of 1 kg. Find his profit percent.
- He receives payment for 1000 g but delivers only 950 g.
- Profit% \(= (1000 - 950)/950 \times 100 = 50/950 \times 100 \approx 5.26\%\).
Example 5 — Discount + Profit (2021-II)
Q: A shopkeeper marks his goods 40% above cost price and then allows a discount of 25% on the marked price. Find his profit percent.
- Let CP = 100. MP = 140. SP = \(140 \cdot 0.75 = 105\).
- Profit% \(= (105 - 100)/100 \times 100 = 5\%\).
Example 6 — Mixed Rate Sale (2020-I)
Q: A man bought 60 pens at ₹10 each. He sold 30 at 20% profit and the rest at 10% loss. Find his net profit/loss percent.
- Total CP = \(60 \cdot 10 = 600\). SP of first 30: \(30 \cdot 12 = 360\). SP of last 30: \(30 \cdot 9 = 270\). Total SP = 630.
- Profit = 30. Profit% = \(30/600 \times 100 = 5\%\).
Example 7 — Marked Price Reverse (2017-I)
Q: A trader allows a 20% discount on the marked price and still gains 12%. If the cost price is ₹400, find the marked price.
- SP \(= 400 \cdot 1.12 = 448\). After 20% discount, \(SP = MP \cdot 0.80\).
- \(MP = 448/0.80 = 560\).
How CDS Tests This Topic
Six archetypes recur: (1) plain profit/loss percent, (2) successive discount, (3) two articles same SP one profit one loss, (4) false weights, (5) discount + markup mixed (find one from others), and (6) mixed-rate sale. Master each and you collect 3-4 marks per paper.
Exam Shortcuts (Pro-Tips)
Shortcut 1 — Successive Discount Formula
Shortcut 2 — Equal SP, Equal %
Same SP, one at \(x\%\) profit, one at \(x\%\) loss → overall loss% = \((x/10)^2\). Always a loss.
Shortcut 3 — Decimal Multipliers
20% profit = multiply CP by 1.20. 15% discount = multiply MP by 0.85. Compose: (MP × 0.85) > CP × 1 → still profitable.
Shortcut 4 — CP = 100 Setup
For multi-step markup/discount problems, set CP = 100. Compute through. Final SP minus 100 is your profit%.
Shortcut 5 — False Weight as Percentage
If dealer uses weight \(W\) for claimed \(W'\), profit% = \((W' - W)/W \times 100\). The denominator is the actual weight he gives.
Common Question Patterns
Pattern 1 — Plain Profit/Loss
Given CP and SP, find profit% or loss% (or vice versa). Apply the basic formula. Always on CP.
Pattern 2 — Successive Discounts
"Discounts of 20% and 10% — single equivalent?" Apply \(d_1 + d_2 - d_1 d_2 / 100\).
Pattern 3 — Equal SP, Profit + Loss
Same SP, equal %s. Net is always loss = \((x/10)^2\). Skip the algebra.
Pattern 4 — Find MP from Discount and Profit
Set CP = 100. Apply profit% to find SP. Apply discount in reverse to find MP. Scale.
Pattern 5 — False Weight
Profit% = \((W' - W)/W \times 100\). The dealer gains by the shortage divided by what he actually delivered.
Preparation Strategy
Week 1. Master CP, SP, MP definitions. Drill 20 problems on basic profit/loss%. Memorise the successive-discount formula and the equal-SP \((x/10)^2\) trick. Always set CP = 100 for multi-step problems.
Week 2. Cover false weights, mixed-rate sales, and discount-with-profit combinations. Layer in Percentage fluency since P&L is percentage applied to commerce.
Mock testing. Take timed CDS papers. Watch for the CP-vs-SP base trap and the sign on losses. Use CDS mock tests for pace.
Drill Profit and Loss in Real Time
CDS mocks with successive discounts, false weights, and mixed-rate sales. Six archetypes — six formulas — reflex.
Start Free Mock TestFrequently Asked Questions
Is profit percent computed on CP or SP?
Always on CP (Cost Price). Profit% \(= (SP - CP)/CP \times 100\). CDS occasionally offers options based on SP — these are distractors. Convert to CP-basis before choosing.
What is the formula for two successive discounts?
\(d_1 + d_2 - d_1 d_2 / 100\). Two discounts of 20% and 10% give net \(20 + 10 - 2 = 28\%\), not 30%. The second discount applies to the reduced (post-first-discount) price.
If two articles sell at the same price, one at \(x\%\) profit and one at \(x\%\) loss, what is the overall result?
Always a loss of \((x/10)^2\%\). At 10% each, the loss is 1%; at 20% each, 4%; at 25% each, 6.25%. The intuition: the loss applies to a higher CP and the profit to a lower CP, so the loss outweighs the profit by a small fixed margin.
How does a "false weight" dishonest dealer earn profit?
He claims to sell 1 kg but uses a lighter weight (say 950 g). He receives the price of 1 kg but delivers only 950 g, gaining 50 g of stock per "kg sold". Profit% \(= 50/950 \times 100 \approx 5.26\%\). The denominator is the actual weight given, not the claimed weight.
How do I find MP given CP and discount-with-profit?
Set CP = 100 (or 1, scale at the end). Compute target SP using the desired profit%. Then \(MP = SP / (1 - d/100)\). Scale back to actual CP. Example: CP = 400, want 12% profit after 20% discount: SP = 448; MP = \(448/0.8 = 560\).
Why is a 20% markup followed by a 20% discount a loss?
Apply the successive-percentage formula: \(20 - 20 - 400/100 = -4\%\). The discount applies to a higher base (MP = 1.2 CP) and so subtracts more in absolute terms than the markup added. Net is 4% below CP.
Which CDS Maths topics connect to Profit and Loss?
Percentage is the direct parent. Ratio and Proportion (especially alligation) appears in mixed-rate problems. SI/CI shares the same "rate × time" structure. Master Percentage first, then this chapter falls into place.