Profit, Loss & Discount
🔒 Log in to trackThe highest-yield arithmetic block in Tier 1. CP–SP basics, successive discounts, the marked-price chain and dishonest-dealer cases appear in nearly every shift; Tier 2 layers on trade chains and price-shift comparisons. Everything reduces to multiplier chips.
One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.
Every formula on one printable page, grouped by subtopic.
5 exam-level questions worked step by step.
69 questions — untimed practice or a timed test with analysis.
Track record in the exam
Questions per shift in recent SSC CGL papers.
Test difficulty mix (69 questions)
Question patterns exams keep repeating
Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.
Find the profit or loss %
very commonCP and SP are given. "Find the profit per cent."
Profit = selling price − cost price.
Divide by the cost price, then × 100.
A cycle bought for ₹850 is sold for ₹1,020. Profit per cent?
Profit = 1020 − 850 = 170
170 ÷ 850 = 1/5
1/5 × 100 = 20% profit
Find the cost price from a profit or loss clue
very common"Had he sold it for ₹960 more, he would have gained 15% instead of losing 5%."
Add the two percents: the extra money equals that % of the cost price.
Then find 1% and scale up.
A scooter is sold at a 5% loss. Sold for ₹960 more, it gives a 15% gain. Find the CP.
Loss 5% to gain 15% is a jump of 20% of CP
20% of CP = 960
1% of CP = 48
CP = 48 × 100 = ₹4,800
Two discounts one after another
very common"Two successive discounts of 20% and 12.5%."
Take the discounts one at a time, each on the new price.
Never just add the discounts.
A sofa marked ₹1,600 gets discounts of 20% and then 12.5%. Selling price?
20% of 1600 = 320, so price = 1280
12.5% of 1280 = 160
1280 − 160 = 1120
SP = ₹1,120
Marked price, discount and profit
very common"A discount of 25% is given and the gain is still 20%. The marked price is what % above cost?"
Start with marked price = 100.
Find the selling price, then the cost price, then compare.
A trader gives 25% discount and still gains 20%. The marked price is what % above the cost price?
Marked price = 100, so SP = 75
SP is 20% above CP, so CP = 75 ÷ 1.2 = 62.5
Marked price is 100 − 62.5 = 37.5 above CP
37.5 ÷ 62.5 × 100 = 60%
Shopkeeper who cheats on weight
common"A milkman sells at cost price but gives only 800 mL per litre."
Find what the customer pays for and what he really gets.
Gain = the cheated amount ÷ the amount actually given × 100.
A milkman sells at cost price but gives only 800 mL for every litre. Gain per cent?
Customer pays for 1000 mL but gets 800 mL
His cost is only for 800 mL
Gain = 200 mL worth
200 ÷ 800 × 100 = 25%
Same selling price, one profit and one loss
common"Two articles sold at ₹1,200 each, one at 25% profit and one at 25% loss."
Find each cost price on its own.
Compare total cost with total selling price.
Two articles sell at ₹1,200 each, one at 25% profit and one at 25% loss. Overall loss per cent?
Profit one: CP = 1200 ÷ 1.25 = 960
Loss one: CP = 1200 ÷ 0.75 = 1600
Total CP = 2560, total SP = 2400, loss = 160
160 ÷ 2560 × 100 = 6.25% loss
Profit added at each step of a chain
occasional"Manufacturer to wholesaler to retailer to customer, each adding a profit %."
Start with 100.
Add each profit on the latest price, one step at a time.
A manufacturer sells at 20% profit, the wholesaler at 25% profit, the retailer at 10% profit. Total rise over manufacturing cost?
Start: 100
+20% → 120
+25% of 120 (30) → 150
+10% of 150 (15) → 165, so 65% above cost
Cost of some articles equals the selling price of others
occasional"The cost of 15 articles equals the selling price of 12 articles."
Take the smaller number of articles and give each a cost of 1.
Find their selling price and compare.
Cost price of 15 articles = selling price of 12 articles. Profit per cent?
Take 12 articles: cost = 12 (₹1 each)
They sell for the cost of 15 articles = 15
Profit = 15 − 12 = 3
3 ÷ 12 × 100 = 25%