Why this topic matters · 8 min read
Profit and Loss is one of the most frequently tested topics in SSC MTS Quant. Expect 2 to 3 questions per paper. Questions are mostly straightforward: find profit percent, selling price, cost price, or discount. Occasionally you get a tricky question involving two successive transactions or false weights. If you know the core formulas and practice 10 to 15 questions, this becomes a sure-shot scoring area.
Basic Terms You Must Know
Cost Price (CP) is what you pay to buy or make something. Selling Price (SP) is what you get when you sell it. If SP is more than CP, you make a Profit. If SP is less than CP, you make a Loss. Marked Price (MP) is the price written on the tag before any discount. These four terms appear in almost every question.
- CP = what you buy it for
- SP = what you sell it for
- Profit = SP minus CP (when SP is greater)
- Loss = CP minus SP (when CP is greater)
- Marked Price = the printed or listed price before discount
- Discount is always calculated on Marked Price, NOT on CP
Key formulas
Profit Percent
Profit% = (Profit / CP) x 100
When: When you know profit amount and CP
Loss Percent
Loss% = (Loss / CP) x 100
When: When you know loss amount and CP
SP from Profit%
SP = CP x (100 + Profit%) / 100
When: When you know CP and profit percent, find SP
SP from Loss%
SP = CP x (100 - Loss%) / 100
When: When you know CP and loss percent, find SP
CP from SP
CP = SP x 100 / (100 + Profit%) or CP = SP x 100 / (100 - Loss%)
When: When SP and percent are given, find CP — very common in SSC MTS
Worked examples
A shopkeeper buys a pen for Rs 80 and sells it for Rs 100. Profit = 100 - 80 = 20. Profit% = (20/80) x 100 = 25%.
A shirt is sold for Rs 540 at a loss of 10%. Find CP. CP = 540 x 100 / (100 - 10) = 54000 / 90 = Rs 600.
Marked Price and Discount
Many SSC MTS questions give you a Marked Price and a Discount percent, then ask for SP. Or they give SP and discount percent and ask for MP. Remember: discount is always on Marked Price. The shopkeeper first marks up the price (above CP), then gives a discount on that marked price. The actual profit depends on both the markup and the discount.
- Discount = Discount% of Marked Price
- SP = MP x (100 - Discount%) / 100
- MP = SP x 100 / (100 - Discount%)
- To find actual profit: compare the final SP with CP
- If both markup% and discount% are given, use the successive percent formula
Key formulas
SP after Discount
SP = MP x (100 - Discount%) / 100
When: MP and discount percent are given
Net effect of Markup and Discount
Net% change = a + b + (ab/100), where a = markup%, b = -discount%
When: When both markup on CP and discount on MP are given — find overall profit or loss percent
Worked examples
MP of a jacket is Rs 1200. Discount is 15%. SP = 1200 x 85/100 = Rs 1020.
A trader marks his goods 25% above CP and gives 10% discount. Net profit% = 25 + (-10) + (25 x -10)/100 = 15 - 2.5 = 12.5%.
Successive Profit or Loss (Two Transactions)
Sometimes a person buys something, then sells it to another person, who then sells it again. Or the same person makes two separate transactions. In these cases, the SP of the first transaction becomes the CP of the second. Just apply the formula step by step. Do not add the two profit percents directly — that is a trap.
- Treat each transaction separately
- SP of first = CP of second
- Calculate each step one by one
- Never add or subtract profit percents across two transactions directly
- If same item is involved in two sales, use: Overall% = a + b + ab/100
Key formulas
Overall effect of two changes
Net% = a + b + (ab/100)
When: Two successive percent changes on same base — profit then profit, or profit then loss etc.
Worked example
A bought a cycle for Rs 1000, sold to B at 10% profit. B sold to C at 5% loss. A sells to B at SP = 1000 x 110/100 = Rs 1100. B sells to C at SP = 1100 x 95/100 = Rs 1045. C paid Rs 1045.
Dishonest Dealer and False Weight
A classic SSC question: a shopkeeper claims to sell at cost price but uses a false weight. For example, he sells 800 grams but claims it is 1000 grams. He still earns a profit because he gives less than what the customer pays for. The profit percent here is calculated on what he actually gives, not on what he claims.
- Profit% = (True weight - False weight) / False weight x 100
- If dealer uses 900g weight instead of 1000g and sells at CP, profit = (1000-900)/900 x 100 = 11.11%
- This type has appeared in SSC exams in recent years
- Remember: denominator is the false (smaller) weight, not the true weight
Key formulas
False Weight Profit%
Profit% = (True weight - False weight) / False weight x 100
When: Dealer sells at CP but cheats on weight
Worked example
A shopkeeper uses a 900g weight instead of 1000g and sells at cost price. Profit% = (1000 - 900) / 900 x 100 = 100/900 x 100 = 11.11%.
⚠ Common mistakes to avoid
- Calculating profit or loss percent on SP instead of CP. Always use CP as the base for percent calculation.
- Applying discount percent on CP instead of MP. Discount is ALWAYS on Marked Price.
- Adding two successive profit percents directly. If profit is 10% then 20%, total is NOT 30% — use the formula: 10 + 20 + (10x20)/100 = 32%.
- In false weight problems, dividing by true weight instead of false weight in the denominator.
- Confusing Loss% formula: using SP in denominator instead of CP. Loss% = Loss/CP x 100, not Loss/SP x 100.
🧠 Memory aids
- CP is the COST you PAY — profit and loss percent are always on this. Think: CP = Captain, everything is compared to the Captain.
- Discount on MP — MP is the Marked (tagged) Price on the product, so discount is on the tag. Simple.
- For double transactions, remember LINK: SP of first is CP of second — like a chain, link them.
- False weight trick: the shopkeeper gives LESS but charges for MORE. Profit = Extra kept / What he actually gave x 100. Denominator is what he gives (false weight).
- Formula shortcut for SP: Profit means ADD the percent, Loss means SUBTRACT. SP = CP x (100 plus or minus %) divided by 100.
🎯 SSC MTS exam tips
- SSC MTS typically asks 2 to 3 questions. At least one will be a direct formula question — find SP or CP from given percent. These should take under 30 seconds each.
- One question often involves discount and marked price. Practice: given SP and discount%, find MP. Use MP = SP x 100 / (100 - Discount%).
- False weight or dishonest shopkeeper questions appear once in a while. If you see the word cheats or false weight — directly use Profit% = (True - False) / False x 100.
- Avoid lengthy calculations. If numbers look messy, check if the answer options are round numbers — often the calculation simplifies with the right formula.
- In exam, if both markup and discount are given as percents, use the net effect formula directly instead of calculating MP first and then SP — saves 30 to 45 seconds per question.
Q1 · medium · PYQ 2017
An article is sold at 30% loss. If the selling price is increased by 50%, then what is the profit percentage?
- 5%
- 12%
- 20%
- 8%
Q2 · medium · PYQ 2017
If the ratio of selling price and cost price is 3 : 4 respectively, then what is the loss percentage?
- 25%
- 20%
- 10%
- 33.33%
Q3 · hard · AI-verified
Two articles are sold at ₹1200 each. One is sold at 20% profit and the other at 20% loss. What is the overall loss percentage on the transaction?
- 0%
- 5%
- 2%
- 4%
Q4 · medium · PYQ 2024
By selling an article for ₹20, a dealer makes a profit of 20%. By how much should he increase his selling price (in ₹, rounded off to two decimal place) so as to make a profit of 30%?
- 3.67
- 2.67
- 4.67
- 1.67
Q5 · medium · PYQ 2024
A dishonest shopkeeper promises to sell his goods at cost price. However, he uses a weight that actually weighs 33% less than what is written on it. Find his profit percentage.
- 48(17/67)%
- 49(17/67)%
- 51(34/67)%
- 50(18/67)%