Profit and Loss is a chapter about trade — what you paid vs. what you received. Everything in this chapter reduces to three prices and their relationships.
Cost Price (CP): What you paid to get the goods. This is your input.
Selling Price (SP): What you actually received when you sold them. This is your output.
Marked Price (MP): The price written on the tag before any discount is applied. The shopkeeper marks it artificially high so that even after giving a discount, they still make a profit.
The logic is simple:
SP > CP → Profit. Profit = SP − CP.SP < CP → Loss. Loss = CP − SP.Profit % and Loss % are always calculated on CP, not on SP. This is the single most exploited trap in SSC exams, and you need to tattoo it on your brain.
Think of it like this: you invest the CP. The return on that investment — profit or loss — is measured against what you invested, not what you recovered. A soldier who deployed 100 soldiers and recovered 120 made a 20% gain on deployment, not on the recovery.
The marked price introduces a two-step chain: first, the shopkeeper marks up from CP to MP; then gives a discount from MP to SP. The net effect on CP determines whether there is profit or loss.
Don't write SP = CP + profit. Instead, think in multipliers. It eliminates separate steps.
| Situation | Relationship |
|---|---|
| 25% Profit | SP = CP × 1.25 |
| 20% Loss | SP = CP × 0.80 |
| 40% Markup | MP = CP × 1.40 |
| 15% Discount | SP = MP × 0.85 |
This approach lets you chain two conditions in one multiplication, which is exactly what the MP-Discount problems require.
This trips candidates up the most. If SP = CP × 1.25, then:
Look — when you get SP and profit%, convert the multiplier to a fraction and flip it. SP = 1200, profit = 25% means CP = 1200 × (100/125) = 960. Do not subtract 25% of SP from SP. That is wrong. It will give you 900, and 900 is wrong.
This is a two-step problem that SSC GD repeats in every paper.
Setup: Shopkeeper marks goods m% above CP, then gives d% discount.
Net profit/loss % is determined by whether the final SP is above or below CP. The cleanest approach is to assume CP = 100 always. Then MP and SP follow automatically.
Example: 30% markup, 20% discount.
You never need a formula. Assume CP = 100, follow the chain.
This is a classic SSC trap: "X fruits bought for Y paise, Z fruits sold for W paise."
The trick is to find per-unit CP and per-unit SP.
(SP per unit − CP per unit) / CP per unit × 100Alternatively, work with a common batch size (LCM of the buy-quantity and sell-quantity).
"Sold 3/4 of goods at 20% profit and 1/4 at 10% loss."
Use weighted average. If CP of the whole lot is 100:
75 × 1.20 = 9025 × 0.90 = 22.5You know CP and the final profit%. That means you know SP. You also know the discount%. Work backwards from SP to MP.
where d is the discount percentage. Remember: SP = MP × (100 − d)/100, so MP = SP reversed through that multiplier.
Whenever you see markup % and discount % together, chain the two multipliers in one shot.
Net effect = (1 + m/100) × (1 − d/100) on CP.
Example: 40% markup, 25% discount = 1.40 × 0.75 = 1.05 → 5% profit.
Standard method: Set up two equations, 3 steps, ~50 seconds. Multiplier chain: One multiplication, ~12 seconds. The answer is the decimal beyond 1.00 — here 0.05 = 5%.
When given SP and profit%, never subtract profit% of SP. Always use:
CP = SP × 100 / (100 + profit%)
For SP = 1200, profit = 25%: CP = 1200 × 100/125 = 1200 × 4/5 = 960.
Standard mistake path: 1200 − 25% of 1200 = 1200 − 300 = 900 (wrong, costs you the mark). Correct fraction flip: 2 steps, 10 seconds.
"11 items bought for 10 paise, 10 items sold for 11 paise" type questions.
Find CP per item and SP per item, then compute profit% directly.
(11/10 − 10/11) ÷ (10/11) × 100(121 − 100) / 100 × 100 (after simplifying with LCM 110) = 21%Alternatively: take LCM of 11 and 10 = 110 items. CP of 110 = 10 × 10 = 100 paise. SP of 110 = 11 × 11 = 121 paise. Profit = 21%. Standard method: 5 steps, ~60 seconds. LCM batch method: 3 steps, ~20 seconds.
When "CP of A items = SP of B items":
Profit% = (A − B) / B × 100
CP of 12 pens = SP of 10 pens → Profit% = (12 − 10)/10 × 100 = 20%.
Standard method (assign unit values, compute SP per pen, calculate %): 4 steps, ~45 seconds. Direct formula: 1 step, ~8 seconds. Valid only when CP of more = SP of fewer (profit scenario) or CP of fewer = SP of more (loss scenario).
For mixed lot problems, convert each fraction of goods into its SP contribution and add.
Rule: Total SP = f₁ × CP₁ × (1 ± p₁/100) + f₂ × CP₂ × (1 ± p₂/100) where f is the fraction of total CP.
With CP = 6000: 3/4 at +20% → 4500 × 1.20 = 5400; 1/4 at −10% → 1500 × 0.90 = 1350. Total SP = 6750. Profit = 750/6000 = 12.5%.
This avoids setting up two separate profit/loss amounts and adding them — cuts 2 steps from the standard approach.
When a Profit & Loss question appears, run this decision tree in 5 seconds:
Step 1 — Identify what's given and what's asked.
CP = SP × 100/(100 + profit%).SP = MP × (100 − d)/100.Step 2 — Assume CP = 100 for any question that doesn't give you actual rupee values. This converts every % problem into arithmetic on simple numbers.
Step 3 — Watch the base. Every percentage in this chapter is on CP unless the question explicitly says "on SP" (rare in SSC GD). Confirm before computing.
Step 4 — Quantity problems (N items bought for X, M items sold for Y): go straight to per-unit CP and SP, or use the LCM batch method.
Step 5 — Check answer against options. If your answer doesn't match any option, you likely took % on the wrong base (SP instead of CP or vice versa). Recompute.
Why this question: Tests the classic "buy-quantity ≠ sell-quantity" format where candidates typically try to set up algebraic equations and lose time.
Solving path: Use LCM batch method. LCM(11, 10) = 110. Buy 110 lichchus: cost = 10 × 10 = 100 paise. Sell 110 lichchus: revenue = 11 × 11 = 121 paise. Profit = 21 paise on CP of 100. Gain% = 21%. Total time under 20 seconds.
Why this question: Markup + Discount chain is the most repeated MP question type in SSC GD. Tests whether you can correctly chain two percentages instead of just adding/subtracting them.
Solving path: Assume CP = 100. MP = 140 (40% above CP). Discount 25% on MP: SP = 140 × 0.75 = 105. Profit = 5, so profit% = 5%. Option (a). Do not add markup and subtract discount directly — that gives 15%, which is wrong.
Why this question: Finding CP from SP is one of the most frequently answered incorrectly in mock data because candidates subtract profit% from SP instead of dividing properly.
Solving path: SP = CP × 125/100. So CP = 1200 × 100/125 = 1200 × 4/5 = ₹960. Option (b). The trap option ₹900 = 1200 × 0.75 — that's what you get if you wrongly subtract 25% of SP.
Why this question: Tests the mixed-lot problem where different portions are sold at different profit/loss rates. Requires weighted calculation, not simple averaging.
Solving path: CP = 6000. Portion 1: ₹4500 sold at +20% → SP = 5400. Portion 2: ₹1500 sold at −10% → SP = 1350. Total SP = 6750. Profit = 750. Profit% = 750/6000 × 100 = 12.5%. Option (a).
Why this question: Fruit/item problems where buy-rate and sell-rate are given in different bundle sizes. Standard in SSC GD and easily solved with per-unit method.
Solving path: CP per orange = 10/5 = ₹2. SP per orange = 10/4 = ₹2.50. Profit per orange = 0.50. Profit% = 0.50/2 × 100 = 25%. Option (b).
Profit% on SP instead of CP. In SSC GD, profit and loss percentages are always on CP unless explicitly stated otherwise. Computing 25% profit on SP = 1200 as 1200 × 0.25 = 300 and subtracting to get CP = 900 is a guaranteed wrong answer.
Adding markup% and discount% for net effect. If markup is 40% and discount is 25%, net is NOT 15%. Net = 1.40 × 0.75 = 1.05 → 5% profit. Percentages on different bases cannot be directly added or subtracted.
Using SP as base for finding MP. When finding marked price: MP = SP × 100/(100 − d%). Using CP as base here instead of working through SP gives wrong MP.
LCM batch size omitted in quantity problems. In "11 bought for 10, 10 sold for 11" problems, many candidates find per-unit CP and SP correctly but then calculate profit% on SP instead of CP. Always divide profit by CP per unit, not SP per unit.
Confusing discount% base. Discount is always on Marked Price, not on CP or SP. A 15% discount means 15% off MP, so SP = MP × 0.85. Applying 15% off CP is a category error.
Incorrect fraction assignment in mixed lot problems. When "3/4 sold at profit and 1/4 at loss," students sometimes calculate 3/4 and 1/4 of the number of items but apply profit/loss percentages on full CP. Always split CP in the same fractions as the goods.