Concept 1
Separate cost, selling and marked price
Cost price (CP) is what the seller pays, including expenses needed to make the item sale-ready. Selling price (SP) is the realised sale amount. Marked price (MP) is the listed amount before discount.
Choose the base: profit or loss percentage is normally based on CP; discount percentage is based on MP.
Concept 2
Profit and loss compare SP with CP
Profit=SP−CP when SP>CP, and loss=CP−SP when SP<CP. Profit%=profit/CP×100; loss%=loss/CP×100.
| Situation | Direct multiplier |
|---|---|
| p% profit | SP=CP(1+p/100) |
| p% loss | SP=CP(1−p/100) |
Concept 3
Reverse the multiplier to recover cost
If SP=₹1,380 at 15% profit, then CP=1380/1.15=₹1,200. Do not subtract 15% of SP because the stated percentage uses CP as its base.
For p% profit, CP=SP×100/(100+p). For p% loss, CP=SP×100/(100−p).
Concept 4
Discount connects marked price to selling price
Discount=MP−SP and discount%=discount/MP×100. Therefore SP=MP(1−d/100). If an item marked ₹2,500 receives 12% discount, SP=2500×0.88=₹2,200.
If both markup and discount are given, move from CP to MP and then MP to SP; never apply both to the same base without justification.
Concept 5
Successive percentages multiply
Two discounts a% and b% produce an equivalent discount a+b−ab/100. Discounts of 20% and 10% leave 0.8×0.9=0.72 of MP, so the equivalent discount is 28%, not 30%.
For any sequence of percentage changes, multiply the remaining or growth factors in order.
Concept 6
A short weight changes the effective selling rate
If a seller charges for 1 kg but gives w grams, and otherwise sells at cost rate, gain%=(1000−w)/w×100. Giving 800 g for the price of 1 kg produces 200/800×100=25% gain.
Denominator warning: actual cost corresponds to the quantity delivered, so divide by w—not by 1000.
Applications
Common examination structures
Overhead expenses
Add transport, repair or tax paid by the buyer to CP when the question treats it as acquisition cost.
Required markup
Set CP=100, apply desired profit to find SP, then divide by the post-discount factor to find MP.
Same SP, one gain and one loss
For equal percentage x and equal SP, the overall result is a loss of x²/100 percent.
Quantity deals
“Buy x, get y free” gives y/(x+y)×100% effective discount when all units have equal marked price.
Worked methods
Examples with reasoning
CP ₹800, SP ₹920
Profit=₹120; profit%=120/800×100=15%.
SP ₹1,530 after 10% loss
CP=1530×100/90=₹1,700.
MP ₹3,000 with discounts 20% and 5%
SP=3000×0.8×0.95=₹2,280; equivalent discount=24%.
Marked 25% above CP, then 10% discount
Let CP=100. MP=125 and SP=112.5, so profit=12.5%.
Two items sold at ₹990 each, one at 10% gain and one at 10% loss
Total CP=900+1100=2000; total SP=1980, so overall loss=1%.
Exam traps
Errors caused by the wrong base
Profit on SP
Unless explicitly stated otherwise, profit percent uses CP.
Adding discounts
Successive discounts act on changing amounts, so multiply factors.
Ignoring expenses
Include expenses that the problem treats as part of acquiring or preparing the item.
Equal percentages cancel
An x% rise and x% fall do not cancel because the second base differs.
Gain-loss pair
One item at x% gain and another at x% loss is not automatically neutral.
False-weight denominator
Compare excess revenue with the cost of the quantity actually delivered.
Original practice
Check understanding after learning
Original syllabus-aligned questions—not claimed previous-year questions.
Rapid revision
The one-minute sheet
- Profit or loss percent normally uses CP; discount percent uses MP.
- SP=CP×profit/loss multiplier; reverse by dividing by that multiplier.
- SP=MP×(1−discount rate).
- Successive changes multiply; do not simply add percentages.
- Two equal-SP sales at x% gain and x% loss give x²/100% loss.
- For short weight w grams per charged kilogram, gain%=(1000−w)/w×100.
Source ledger
Official foundations
- SSC CGL official syllabus: Mathematical Abilities
- NCERT official mathematics exemplar directory
- NCERT official textbook portal
Explanations, worked examples and practice are original. Official references are credited and not reproduced. Drafted 24 September 2026.
Simple and compound interest: growth over time and instalments.