Profit, Loss & Discount — SSC CGL Quantitative Aptitude

PLD is the Percentage chapter wearing a shopkeeper's apron. Three prices — cost price (CP), marked price (MP), selling price (SP) — connected by two percentages: profit/loss (between CP and SP) and discount (between MP and SP). Keep every move as a multiplying factor and PLD questions become single-line calculations.

1. What SSC actually asks

Tier 1: 2–3 Q · Tier 2: 3–4 Q. The recurring templates:

1. Straight chain — CP, %profit, discount, MP relations.
2. Successive discounts — "30% + 20%" is not 50%.
3. Markup + discount → net profit — the shopkeeper's game.
4. Two items, same SP — one at +x%, one at −x% → always a net loss.
5. False weights — sells at "cost price" but uses a 900 g weight.
6. SP–SP comparisons — "sold for ₹X at 10% loss; to gain 15%, sell at?"
7. CP of y articles = SP of x articles type.

2. The factor chain

$\text{SP}=\text{CP}\times \left(1+\frac{g}{100}\right)\text{(gain g\%)}\text{SP}=\text{MP}\times \left(1-\frac{d}{100}\right)\text{(discount d\%)}$

So the whole shop runs on one line:

$\text{CP}\stackrel{\times (1+g/100)}{\to }\text{SP}\stackrel{\times (1-d/100)}{\leftarrow }\text{MP}$

Markup: MP = CP × (1 + m/100). Combining: $(1+m)(1-d)=(1+g)$ in factor form — the shopkeeper equation.

Example. A trader marks 40% above cost and gives 15% discount. Net gain? $\frac{7}{5}\times \frac{17}{20}=\frac{119}{100}$ → 19%.

Profit/loss is always on CP unless the question explicitly says otherwise. "Profit on SP" wording is a deliberate trap — convert: profit% on CP = $\frac{p}{100-p}\times 100$ when p is given on SP.

3. Successive discounts

Two discounts $d_1,d_2$: net discount $=d_1+d_2-\frac{d_1{d}_2}{100}$ (same formula as successive percentage change, both negative).

• 30% + 20% → $30+20-6=44\%$, never 50%.
• Three discounts: chain the factors: $0.7\times 0.8\times 0.9=0.504$ → 49.6%.
• A single discount is always better for the buyer than the same total split — and the order of discounts never matters (multiplication commutes).

4. The classic traps as formulas

Two items, same SP, +x% and −x%: net result is always a loss of $\frac{x^2}{100}\%$ on the whole transaction. Sold two horses at ₹9,900 each, one at +10%, one at −10% → net loss = 1%.

False weight (sells at CP with weight w instead of 1000 g):

$\text{Gain}\%=\frac{\text{true}-\text{false}}{\text{false}}\times 100=\frac{1000-w}{w}\times 100$

Uses 800 g → $\frac{200}{800}=25\%$ gain (note: divide by the false weight, not 1000).

CP of x articles = SP of y articles (x > y → profit):

$\text{Gain}\%=\frac{x-y}{y}\times 100$

CP of 25 pens = SP of 20 pens → gain = $\frac{5}{20}=25\%$.

Same-SP re-pricing: "Sold at ₹1,080 with 10% loss; SP for 15% gain?" CP = 1080/0.9 = 1200 → new SP = 1200 × 1.15 = ₹1,380. Always route through CP.

Profit rupees = discount rupees questions: use MP − SP = discount amount, SP − CP = profit amount and solve the little linear system.

5. Solved PYQ-style examples

Q1. A shopkeeper buys at ₹640 and sells at ₹720. Later he raises the price so the profit % doubles. New SP? Solution. Profit% = 80/640 = 12.5% → doubled = 25% → SP = 640 × 1.25 = ₹800.

Q2. After two successive discounts of 20% and 25%, an item sells at ₹540. The marked price? Solution. $MP\times 0.8\times 0.75=540$ → $MP\times 0.6=540$ → MP = ₹900.

Q3. A dealer professes to sell at cost price but uses a weight of 940 g for a kg. Gain%? Solution. $\frac{60}{940}\times 100=\frac{6000}{940}\approx 6.38\%$ → 6 ⁷⁄₄₇ %.

Q4. By selling 33 m of cloth, a trader gains the SP of 11 m. Gain%? Solution. Gain = SP of 11 m; SP of 33 m = CP of 33 m + SP of 11 m → SP of 22 m = CP of 33 m → per-metre SP/CP = 33/22 = 3/2 → gain = 50%.

Q5. An article marked ₹1,500 is sold at 12% discount, yielding a 10% profit. The cost price? Solution. SP = 1500 × 0.88 = 1320 = CP × 1.10 → CP = ₹1,200.

Q6 (Tier 2). A man sells two scooters at ₹48,510 each, gaining 10% on one and losing 10% on the other. Net gain/loss? Solution. Same-SP ± x% → loss of $\frac{100}{100}=1\%$ of total CP. CPs: 44,100 and 53,900 → total CP 98,000, total SP 97,020 → loss ₹980 = 1% loss ✓.

6. Exam protocol

1. Write the chain CP → (gain factor) → SP ← (discount factor) ← MP before touching numbers.
2. Convert every % to a fraction (Percentage chapter table) — SSC's numbers are built for it.
3. Same-SP pair → answer is a $x^2/100$ loss, no computation.
4. False weight → divide by the false weight.
5. Route all re-pricing through CP; never chain SP → SP directly.
6. 40-second cap in Tier 1; the template identifies itself in the first read.