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Numerical Ability · AFCAT

NA03 — Profit, Loss & Discount

💰 Numerical Ability – NA03 AFCAT Level ★ High Priority

📌 AFCAT Focus: NA03 is a direct-formula chapter. 2–3 questions per paper. Master SP = CP×(100±%)/100, successive discount formula, and dishonest dealer (false weight) shortcut. AFCAT rarely tests GST deeply — focus on discount and profit/loss cycles. Worked examples are essential for speed.

1. Profit & Loss

Fig. 1.1 — Profit & Loss: Relationship Between CP, SP, MP & Discount

Core Profit & Loss Formulas:
● Profit = SP − CP    Loss = CP − SP
● Profit% = (Profit/CP) × 100    Loss% = (Loss/CP) × 100
● SP = CP × (100 + Profit%) / 100    SP = CP × (100 − Loss%) / 100
● CP = SP × 100 / (100 + Profit%)    CP = SP × 100 / (100 − Loss%)
● Dishonest dealer (false weight): Gain% = (True wt − False wt) / False wt × 100

🏭 Dishonest Dealings

False weight: Dealer uses 900g weight but claims 1kg. Gain% = (1000−900)/900 × 100 = 11.11%
General formula: Gain% = Error/(True value − Error) × 100
Buying cheap, selling dear: If buys at x% less and sells at y% more, overall profit% = x + y + xy/100
Always find CP and SP first before computing %

🏭 Multiple Transactions

Article passes through hands: Seller1's SP = Seller2's CP
Apply each profit/loss sequentially to the new CP
Example: A sells to B at 10% profit, B sells to C at 20% profit. If A's CP = Rs 100: A→B at Rs 110; B→C at Rs 110×1.20 = Rs 132
For overall single transaction: use net % formula

✎ Worked Example — Profit & Loss

A shopkeeper marks an article 40% above CP and then gives a 25% discount. Find profit%.

Let CP = Rs 100. MP = 100 + 40% = Rs 140
SP = MP × (100−25)/100 = 140 × 75/100 = Rs 105
Profit = SP − CP = 105 − 100 = Rs 5
Profit% = (5/100) × 100 = 5%

✔ Profit = 5%

DISCOUNT & TAXATION

2. Discount & Taxation

Topic BDiscount FormulasAFCAT Direct

Discount

Discount = MP − SP
Discount% = (Discount/MP) × 100 ← Always on MP, not CP!

Successive Discounts

Two discounts d1% and d2% successively → Net discount = d1 + d2 − d1×d2/100
e.g., 20% and 25% = 20+25−5 = 40% single equivalent discount

GST Basics

GST (Goods & Services Tax): Amount paid = Original price + GST%. e.g., Rs 500 item at 18% GST → Pay Rs 500 + Rs 90 = Rs 590. For AFCAT: GST = % of the taxable value (ex-GST price).

✎ Worked Example — Successive Discount

A television is listed at Rs 25,000. Successive discounts of 20% and 10% are given. What is the selling price?

After 20% discount: 25,000 × 80/100 = Rs 20,000
After 10% further discount: 20,000 × 90/100 = Rs 18,000
(Net equivalent discount = 20+10−2 = 28%; SP = 25,000×72/100 = 18,000 ✓)

✔ Selling Price = Rs 18,000

Topic CGST & VAT — Complete CoverageAFCAT Theory

GST Concept

Goods & Services Tax — a unified indirect tax on supply of goods/services in India (replaced VAT, service tax, excise). Implemented: 1 July 2017.

CGST + SGST

GST is split: CGST (Central GST) + SGST (State GST). For intra-state supply: Total GST = CGST + SGST (each = half the total GST rate).
E.g. 18% GST = 9% CGST + 9% SGST

IGST

For inter-state supply: IGST (Integrated GST) = entire GST goes to centre. E.g. selling from Maharashtra to Delhi → 18% IGST (not split).

GST Slabs

GST rates in India: 0%, 5%, 12%, 18%, 28%. Essentials (food grains) = 0%. Luxury goods = 28%. Most services = 18%.

GST Calculation

Amount with GST = Original price × (1 + GST%/100)
GST amount = Original price × GST%/100
Original from final: Price = Final amount × 100 / (100 + GST%)

VAT Concept

Value Added Tax — tax levied at each stage of production/sale on the VALUE ADDED at that stage (not on full price). Predecessor to GST in India. Still used in some states for petrol/alcohol. VAT is borne by the end consumer.

VAT Formula

VAT amount = Cost Price × VAT%/100
Selling price (with VAT) = CP × (1 + VAT%/100)
E.g. CP = Rs 500, VAT = 12% → SP = 500 × 1.12 = Rs 560

✎ Worked Example — GST Calculation

A mobile phone costs Rs 15,000 (ex-GST). GST rate = 18%. Find: (a) GST amount, (b) price paid by customer, (c) CGST and SGST amounts (intra-state sale).

GST amount = 15,000 × 18/100 = Rs 2,700
Price paid = 15,000 + 2,700 = Rs 17,700
CGST = 9% of 15,000 = Rs 1,350 | SGST = 9% of 15,000 = Rs 1,350
(CGST + SGST = Rs 2,700 = total GST ✓)

✔ GST = Rs 2,700 | Final price = Rs 17,700 | CGST = SGST = Rs 1,350 each

✎ Worked Example — Dishonest Dealer (Faulty Weight)

A shopkeeper claims to sell at cost price but uses a weight of 800 g instead of 1 kg. Find his actual profit percentage.

He gives 800g but charges for 1000g (1 kg).
Gain% = (True weight − False weight) / False weight × 100
= (1000 − 800) / 800 × 100 = 200/800 × 100 = 25%
Alternative: He gets paid for 1000g but only gives 800g, so profit on 800g = 200g worth.
Profit% = 200/800 × 100 = 25%

✔ Profit = 25% (even while "selling at cost price")

📐 Formula Sheet — NA03

Profit & Loss Core

Profit% = (SP−CP)/CP × 100
SP = CP × (100+P%)/100
CP = SP × 100/(100+P%)
Loss: replace + with −

Marked Price & Discount

SP = MP × (100−d%)/100
Discount% always on MP
Successive d1,d2: net = d1+d2−d1d2/100
Profit% always on CP

Dishonest Dealer

Uses false weight w instead of W:
Gain% = (W−w)/w × 100
Sells at CP but uses 900g as 1kg:
Gain = 100/900 × 100 = 11.11%

Useful Shortcuts

Mark up x%, discount y% → Profit/Loss% = x−y−xy/100
If profit% = loss%: no overall gain/loss only if same CP
Sell 2 items, each at Rs X: one 20% gain, one 20% loss → overall 4% loss

GST & Tax

GST Amount = Price × Rate%/100
Total paid = Price + GST amount
CGST + SGST = Total GST
Ex-GST price = Incl. price × 100/(100+GST%)

Common Traps

Discount% → always on MP
Profit%/Loss% → always on CP
Two same% items: P + L = net loss
Overall P/L ≠ average of individual P/L%

📝 Topic-Wise PYQs — NA03

Q1. An article is sold for Rs 336 at a profit of 12%. Find the cost price. AFCAT PYQ

(a) Rs 280(b) Rs 300(c) Rs 312(d) Rs 295

✔ Answer: (b) Rs 300

CP = SP × 100/(100+12) = 336 × 100/112 = 336/1.12 = Rs 300.

Q2. A shopkeeper gives successive discounts of 10% and 15%. What is the single equivalent discount? AFCAT PYQ

(a) 23%(b) 24%(c) 25%(d) 23.5%

✔ Answer: (d) 23.5%

Net = d1+d2−d1×d2/100 = 10+15−(10×15/100) = 25−1.5 = 23.5%.

Q3. A trader marks 25% above CP and gives 20% discount. Find his profit or loss%. AFCAT PYQ

(a) 5% loss(b) 0% (no profit/loss)(c) 5% profit(d) 4% profit

✔ Answer: (b) 0%

Using formula: Profit% = x−y−xy/100 = 25−20−(25×20)/100 = 5−5 = 0%. Alternatively: CP=100, MP=125, SP=125×0.8=100. SP=CP, so no profit or loss.

Q4. A dealer uses a weight of 900 g instead of 1 kg and sells at cost price. His gain% is: ⚡ Tricky

(a) 10%(b) 11.11%(c) 9.09%(d) 12.5%

✔ Answer: (b) 11.11%

Gain% = (True wt − False wt)/False wt × 100 = (1000−900)/900 × 100 = 100/900 × 100 = 11.11%.

Q5. Two items sold at Rs 990 each: one at 10% profit, another at 10% loss. Net result is: ⚡ Tricky

(a) No profit, no loss(b) 1% profit(c) 1% loss(d) 2% loss

✔ Answer: (c) 1% loss

When same SP & same %: Net loss = (common%)²/100 = 10²/100 = 1% loss. CP1 = 990×100/110 = 900; CP2 = 990×100/90 = 1100. Total CP = 2000, Total SP = 1980. Loss = 20, Loss% = 20/2000×100 = 1%.

🧠 Quick Memory Chart — NA03

💰 Profit & Loss

P% = (SP−CP)/CP ×100
SP = CP×(100+P%)/100
CP = SP×100/(100+P%)
P%/L% always on CP
Discount% always on MP

💰 Discount

Successive d1,d2: d1+d2−d1d2/100
Mark x% up, discount y%: x−y−xy/100
Same SP, same %: loss = %²/100
MP ≥ SP ≥ CP (normally)

💰 Shortcuts

Dishonest weight: (W−w)/w ×100
Sell 2 at same SP & same %: always loss
20% P then 20% L = 4% loss
33.3% gain = buy 3, sell 4

📝 Mock Tests 🎯 Subject Quiz ✈️ Telegram