Percentage, Profit and Loss
Why This Chapter Matters
Percentage and Profit/Loss together give 4-6 questions in every SSC exam. These appear directly and inside data interpretation, discount problems, and successive change problems.
Core Concepts
1. Percentage Basics
Percentage means "per hundred". x% = x/100.
To convert fraction to %: multiply by 100.
To convert % to fraction: divide by 100.
% change formula:
% increase = (Increase/Original) × 100
% decrease = (Decrease/Original) × 100
Finding value after % change:
New value = Original × (1 + r/100) for increase
New value = Original × (1 - r/100) for decrease
2. Successive Percentage Change
If a value increases by a% then b%:
Net % change = a + b + ab/100
Example: 20% increase then 25% increase → 20+25+(20×25)/100 = 50% net increase
If one is increase (+) and one is decrease (-), use negative sign:
20% increase then 20% decrease → 20+(-20)+(20×(-20))/100 = -4% net (4% decrease)
3. Profit and Loss
Cost Price (CP): what you pay to buy
Selling Price (SP): what you sell for
Profit: SP > CP → Profit = SP - CP
Loss: SP < CP → Loss = CP - SP
Formulas:
Profit% = (Profit/CP) × 100 = ((SP-CP)/CP) × 100
Loss% = (Loss/CP) × 100 = ((CP-SP)/CP) × 100
SP = CP × (1 + Profit%/100)
SP = CP × (1 - Loss%/100)
CP = SP × 100/(100 + Profit%)
CP = SP × 100/(100 - Loss%)
4. Marked Price and Discount
Marked Price (MP): printed price / list price
Discount = MP - SP
Discount% = (Discount/MP) × 100
SP = MP × (1 - Discount%/100)
Profit after discount:
SP = MP × (1 - d/100) | CP is given separately
Profit% = ((SP-CP)/CP) × 100
5. Important Shortcuts
Selling two articles at same price, one at x% profit and one at x% loss:
Net result is always LOSS = x²/100 %
Example: two items sold at Rs 100 each, one at 20% profit and one at 20% loss → Loss = 400/100 = 4%
If a shopkeeper uses false weights:
Profit% = (True weight - False weight)/False weight × 100
Successive discounts d1% and d2%:
Net discount = d1 + d2 - d1×d2/100
Solved Examples
Q1: A shopkeeper marks goods 25% above cost and gives 10% discount. Profit%?
Let CP=100. MP=125. SP=125×0.9=112.5. Profit=12.5%. Answer: 12.5%
Q2: Article bought for Rs 720, sold at 15% loss. SP?
SP = 720 × (1-15/100) = 720 × 0.85 = Rs 612
Q3: Successive discounts of 20% and 10%. Net discount?
Net = 20+10 - 20×10/100 = 30 - 2 = 28%
PYQs (SSC)
SSC CGL 2023: A sold an article to B at 20% profit. B sold to C at 10% loss. If C paid Rs 2160, what did A pay?
B's SP = C's CP = 2160. B's CP: 2160 = CP_B × 0.9 → CP_B = 2400.
A's SP = B's CP = 2400. A's CP: 2400 = CP_A × 1.2 → CP_A = 2000.
SSC CGL 2022: A tradesman gives 4% discount but uses weights 10% less than marked. Net profit%?
True weight used = 90g per 100g. Gain in weight = 10/90 × 100 = 11.11%
SP with discount = 0.96 of MP. Net profit% = (0.96 × 111.11 - 100) = 6.67%