Percentage, Profit & Loss and Discount

Percentage का अर्थ है "per hundred" (प्रति सौ)। यह किसी संख्या को 100 के आधार पर व्यक्त करने का तरीका है।

Example:

• 25% means 25 out of 100 = 25/100 = 1/4
• 50% means 50 out of 100 = 50/100 = 1/2
• 75% means 75 out of 100 = 75/100 = 3/4

Key Point: Percentage always compares a part to a whole (100).

• To find X% of Y: (X/100) × Y
• To find what % of Y is X: (X/Y) × 100
• To find value after X% increase: Original × (100 + X)/100
• To find value after X% decrease: Original × (100 − X)/100
• To find original value before X% increase: New × 100/(100 + X)
• To find original value before X% decrease: New × 100/(100 − X)

Example 1: What is 20% of 500? → (20/100) × 500 = 100

Example 2: What % is 30 of 150? → (30/150) × 100 = 20%

• Percentage Increase: (New − Original) / Original × 100
• Percentage Decrease: (Original − New) / Original × 100

Important: Always use Original Value as the denominator.

Example 1: A price increases from ₹200 to ₹250. What is the percentage increase?

• Change = 250 − 200 = 50
• % Increase = (50/200) × 100 = 25%

Example 2: A price decreases from ₹250 to ₹200. What is the percentage decrease?

• Change = 250 − 200 = 50
• % Decrease = (50/250) × 100 = 20%

When two or more percentage changes are applied one after another, we use successive percentage formula.

Where A and B are percentage changes (positive for increase, negative for decrease).

Example 1: A number is increased by 10% and then by 20%. What is the net percentage change?

• Net = 10 + 20 + (10×20)/100 = 30 + 2 = 32% increase

Example 2: A number is increased by 10% and then decreased by 10%. What is the net change?

• Net = 10 + (−10) + (10×−10)/100 = 0 − 1 = −1% (1% decrease)

For three successive changes: Apply formula twice: First combine two, then with the third.

• Cost Price (CP) — क्रय मूल्य: वह मूल्य जिस पर कोई वस्तु खरीदी जाती है।
• Selling Price (SP) — विक्रय मूल्य: वह मूल्य जिस पर कोई वस्तु बेची जाती है।
• Profit (Gain) — लाभ: SP > CP → Profit = SP − CP
• Loss — हानि: CP > SP → Loss = CP − SP

• If Profit% is given: SP = CP × (100 + Profit%)/100
• If Loss% is given: SP = CP × (100 − Loss%)/100
• To find CP when SP and Profit% are given: CP = SP × 100/(100 + Profit%)
• To find CP when SP and Loss% are given: CP = SP × 100/(100 − Loss%)

Example 1: CP = ₹200, Profit% = 25% → SP = 200 × 125/100 = ₹250

Example 2: CP = ₹200, Loss% = 20% → SP = 200 × 80/100 = ₹160

Important: Profit/Loss percentage is always calculated on Cost Price (CP), unless otherwise specified.

Example 1: CP = ₹200, SP = ₹250 → Profit = ₹50 → Profit% = (50/200) × 100 = 25%

Example 2: CP = ₹200, SP = ₹160 → Loss = ₹40 → Loss% = (40/200) × 100 = 20%

Example 3: If an article is sold at a profit of 20%, and the profit is ₹40, find CP.

• 20% of CP = 40 → CP = 40 × 100/20 = ₹200

• Marked Price (MP) — अंकित मूल्य: वह मूल्य जो किसी वस्तु पर लिखा/अंकित होता है। (List Price)
• Discount — छूट: MP पर दी जाने वाली कटौती। Discount = MP − SP
• Discount% — छूट प्रतिशत: (Discount / MP) × 100

Example: MP = ₹500, Discount% = 20%

• Discount = 20% of 500 = (20/100) × 500 = ₹100
• SP = MP − Discount = 500 − 100 = ₹400

• SP after Discount: SP = MP × (100 − Discount%)/100
• MP when SP and Discount% given: MP = SP × 100/(100 − Discount%)
• Discount when MP and SP given: Discount = MP − SP
• Discount% when MP and SP given: Discount% = (MP − SP)/MP × 100

Example 1: MP = ₹600, Discount% = 15% → SP = 600 × 85/100 = ₹510

Example 2: SP = ₹850, Discount% = 15% → MP = 850 × 100/85 = ₹1000

When two or more discounts are applied one after another, they are called successive discounts.

Formula:

Where A and B are discount percentages.

Example 1: Two successive discounts of 10% and 20%. What is the net discount?

• Net = 10 + 20 − (10×20)/100 = 30 − 2 = 28%

Example 2: MP = ₹1000, discounts of 10% and 20% applied successively.

• After 10%: SP1 = 1000 × 90/100 = ₹900
• After 20%: SP2 = 900 × 80/100 = ₹720
• Net Discount = 1000 − 720 = ₹280 → 28%

Important: Successive discounts are not additive (10% + 20% ≠ 30% discount).

• Percentage: (Part/Whole) × 100
• Percentage Change: (Change/Original) × 100
• Successive Percentage: A + B + (A×B)/100
• Profit: SP − CP (when SP > CP)
• Loss: CP − SP (when CP > SP)
• Profit%: (Profit/CP) × 100
• Loss%: (Loss/CP) × 100
• SP from Profit%: CP × (100 + P%)/100
• SP from Loss%: CP × (100 − L%)/100
• Discount: MP − SP
• Discount%: (Discount/MP) × 100
• SP after Discount: MP × (100 − D%)/100
• Successive Discount: A + B − (A×B)/100

• Trap 1: Percentage increase and decrease of same percentage are equal → ❌ 10% increase + 10% decrease = 1% net decrease (not 0%)
• Trap 2: Profit% = (Profit/SP) × 100 → ❌ Always Profit% = (Profit/CP) × 100
• Trap 3: Discount% = (Discount/SP) × 100 → ❌ Always Discount% = (Discount/MP) × 100
• Trap 4: Successive discounts are additive → ❌ 10% + 20% ≠ 30% (actual = 28%)
• Trap 5: SP = MP − Discount% → ❌ SP = MP × (100 − D%)/100
• Trap 6: CP = SP × (100 + P%)/100 → ❌ CP = SP × 100/(100 + P%)

What is 15% of 200?

• A. 15
• B. 20
• C. 30
• D. 35

Explanation: (15/100) × 200 = 30.

A price increases from ₹80 to ₹100. What is the percentage increase?

• A. 20%
• B. 25%
• C. 30%
• D. 40%

Explanation: Change = 20, Original = 80 → (20/80) × 100 = 25%.

A number is increased by 10% and then decreased by 10%. What is the net change?

• A. 0%
• B. 1% increase
• C. 1% decrease
• D. 10% decrease

Explanation: 10 + (−10) + (10×−10)/100 = 0 − 1 = −1%.

An article is bought for ₹200 and sold for ₹250. What is the profit percentage?

• A. 20%
• B. 25%
• C. 30%
• D. 40%

Explanation: Profit = 250−200 = 50; Profit% = (50/200)×100 = 25%.

An article is bought for ₹400 and sold at a loss of 20%. What is the SP?

• A. ₹320
• B. ₹360
• C. ₹400
• D. ₹480

Explanation: SP = 400 × (100−20)/100 = 400 × 80/100 = ₹320.

An article marked at ₹500 is sold for ₹400. What is the discount percentage?

• A. 10%
• B. 15%
• C. 20%
• D. 25%

Explanation: Discount = 500−400 = 100; Discount% = (100/500)×100 = 20%.

Two successive discounts of 10% and 20% are given. What is the net discount percentage?

• A. 28%
• B. 30%
• C. 22%
• D. 25%

Explanation: Net = 10 + 20 − (10×20)/100 = 30 − 2 = 28%.

An article is marked at ₹600. After a discount of 20%, it is sold. If the profit is 20%, find the CP.

• A. ₹360
• B. ₹400
• C. ₹450
• D. ₹480

Explanation: SP after discount = 600 × 80/100 = ₹480. Profit% = 20% → CP = SP × 100/(100+20) = 480 × 100/120 = ₹400.

Successive Percentage:

• Net = A + B + (A×B)/100 (with signs)

Profit & Loss:

• Profit = SP − CP | Loss = CP − SP
• SP = CP × (100+P%)/100 | SP = CP × (100−L%)/100

Discount:

• Discount = MP − SP | Discount% = (Discount/MP) × 100
• SP = MP × (100−D%)/100
• Successive Discount = A + B − (A×B)/100

Exam Formula:

UGC NET में Percentage, Profit & Loss और Discount के questions application-based और formula-based होते हैं।