Profit & Loss

Section A · Futures First International — Market Trading Intern OA

📌 What Has Been Asked (OA & Rounds)

Format	Typical Question Style
OA (MCQ)	"A shopkeeper buys at ₹800, marks up 25%, gives 10% discount. Find profit%."
OA	"Selling an article at ₹540 gives 20% profit. At what price should it be sold for 30% profit?"
OA	"By selling 12 oranges, a vendor gains the CP of 3 oranges. Profit%?"
OA	"An article is sold at successive discounts of 20% and 10%. If MP is ₹500, find SP."
Buzzer Round	"CP = 250, SP = 300. Profit%?" → must answer in 3 seconds
Interview	"If I buy 10 items at ₹5 each and sell 8 at ₹8 each, what's my position?" — tests trading P&L intuition

🧠 Core Concepts

1. Fundamental Formulas

Profit = SP − CP          Loss = CP − SP

Profit% = (Profit / CP) × 100
Loss%   = (Loss / CP) × 100

SP = CP × (1 + P%/100)    [if profit]
SP = CP × (1 − L%/100)    [if loss]

2. Marked Price & Discount

Discount = MP − SP
Discount% = (Discount / MP) × 100

SP = MP × (1 − D%/100)

Full chain:

CP → (markup%) → MP → (discount%) → SP → compare with CP → Profit or Loss

3. Successive Discounts

Two successive discounts of d₁% and d₂% are equivalent to a single discount of:

d₁ + d₂ − (d₁ × d₂)/100  %

Example: 20% and 10% → 20 + 10 − 200/100 = 28%

4. Using Multipliers (Fastest)

Action	Multiplier
20% profit	CP × 1.2
15% loss	CP × 0.85
25% markup	CP × 1.25
10% discount	MP × 0.9

Chain example: CP = 800, markup 25%, discount 10% → SP = 800 × 1.25 × 0.9 = 800 × 1.125 = 900 → Profit = 100 → Profit% = 12.5%

⚡ Speed Tricks for Futures First

Trick 1: "By selling N items, gain equals CP of M items"

Profit% = (M / N) × 100

Example: By selling 12 oranges, gain = CP of 3 oranges → Profit% = 3/12 × 100 = 25%

Trick 2: "CP of N items = SP of M items"

Profit% = [(N − M) / M] × 100     (if N > M, it's profit)
Loss%   = [(M − N) / M] × 100     (if M > N, it's loss)

Example: CP of 20 = SP of 16 → Profit% = (20−16)/16 × 100 = 25%

Trick 3: Markup × Discount = Net Effect

If markup = M% and discount = D%:

Net% on CP = M − D − (M×D)/100

Positive = profit, negative = loss.

Trick 4: "Selling at two different prices"

"Sold at 20% profit → SP₁. To get 30% profit → SP₂?"

SP₂/SP₁ = (100 + 30)/(100 + 20) = 130/120 = 13/12
SP₂ = SP₁ × 13/12

No need to find CP first!

Trick 5: Dishonest dealer

"Claims to sell at CP but uses 900g weight instead of 1000g"

Profit% = (True weight − False weight) / False weight × 100
       = (1000 − 900) / 900 × 100 = 11.11%

🎯 What Can Be Asked (Variations)

"A man sells two articles at ₹1000 each, one at 20% profit and other at 20% loss. Net gain/loss?" → Always a loss when SP is same. Loss% = (20²/100)% = 4% on total CP.
- CP₁ = 1000/1.2 = 833.33, CP₂ = 1000/0.8 = 1250. Total CP = 2083.33, Total SP = 2000. Loss = 83.33
"Goods worth ₹6000 are sold at 10% profit and 10% loss. Mix of items — find overall result"
"A shopkeeper marks goods 40% above CP. What discount% should he give to earn 12% profit?" → 1.4 × (1 − D/100) = 1.12 → 1 − D/100 = 0.8 → D = 20%
"An article was sold at a loss of 10%. Had it been sold for ₹90 more, profit would have been 5%. Find CP." → 0.05CP − (−0.10CP) = 90 → 0.15CP = 90 → CP = 600

📝 Practice Questions (with Answers)

Q1. A merchant marks his goods 30% above CP and gives 15% discount. Find his profit%.

A: Net = 30 − 15 − (30×15)/100 = 30 − 15 − 4.5 = 10.5%

Q2. CP of 15 pens = SP of 12 pens. Find profit%.

A: Profit% = (15−12)/12 × 100 = 25%

Q3. An item is sold for ₹480 at 20% profit. What is the CP?

A: CP = 480/1.2 = ₹400

Q4. A trader sells at 10% profit. If CP were 10% less and SP ₹6 more, profit would be 40%. Find original CP.

A: Let CP = x. SP = 1.1x. New CP = 0.9x. New SP = 1.1x + 6 = 1.4 × 0.9x = 1.26x. 1.1x + 6 = 1.26x → 0.16x = 6 → x = ₹37.50

Q5. Successive discounts of 30% and 20% on ₹1000.

A: 1000 × 0.7 × 0.8 = ₹560 (equivalent single discount = 44%)

Q6. A man buys a dozen eggs at ₹12 and sells at ₹1.25 each. Profit%?

A: CP = ₹12, SP = 12 × 1.25 = ₹15. Profit% = 3/12 × 100 = 25%

🔑 Exam Strategy

P&L questions are high-frequency in FF — expect 2-3 in Section A
Use multiplier chains (CP × markup × discount) — avoids errors
"CP of N = SP of M" trick saves 20+ seconds — pattern-match this shape instantly
For "sold at X% profit, to get Y% profit" → use ratio of (100+Y)/(100+X) — never find CP
Trap alert: "Sold at same price, one at X% profit, other at X% loss" → always a net loss = X²/100 %

03_profit_and_loss.md