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Percentages, Profit & Loss
Course: CAT 2026/2027 — 99+ Percentile MBA Master Target Pass • Subject: Quantitative Aptitude
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English / हिन्दी / मराठी
Concept Notes: Concept of Base Percentage
Quantitative Aptitude and Mathematical point-wise notes for Concept of Base Percentage under Percentages, Profit & Loss, calibrated for CAT 2026/2027 — 99+ Percentile MBA Master Target Pass.
GradeUP PRO Academic Intelligence
English / हिन्दी / मराठी
Concept Notes: Successive Percentage Changes
Quantitative Aptitude and Mathematical point-wise notes for Successive Percentage Changes under Percentages, Profit & Loss, calibrated for CAT 2026/2027 — 99+ Percentile MBA Master Target Pass.
GradeUP PRO Academic Intelligence
English / हिन्दी / मराठी
Concept Notes: Discount & Marked Price
Quantitative Aptitude and Mathematical point-wise notes for Discount & Marked Price under Percentages, Profit & Loss, calibrated for CAT 2026/2027 — 99+ Percentile MBA Master Target Pass.
GradeUP PRO Academic Intelligence
English / हिन्दी / मराठी
Concept Notes: Partnership & Profit Sharing
Comprehensive point-wise study notes for Partnership & Profit Sharing under Percentages, Profit & Loss, strictly calibrated for CAT 2026/2027 — 99+ Percentile MBA Master Target Pass.
Grade UP Expert Desk
Hindi
Revision Notes: Concept of Base Percentage High-Yield Summary (Part 1)
Comprehensive revision notes covering main definitions, derivations and key examples for Concept of Base Percentage.
NCERT Solutions
English
Revision Notes: Concept of Base Percentage High-Yield Summary (Part 2)
Comprehensive revision notes covering main definitions, derivations and key examples for Concept of Base Percentage.
NPTEL Study Circle
Hindi
Revision Notes: Concept of Base Percentage High-Yield Summary (Part 3)
Comprehensive revision notes covering main definitions, derivations and key examples for Concept of Base Percentage.
Sovereign Educational Repository
English
Revision Notes: Concept of Base Percentage High-Yield Summary (Part 4)
Comprehensive revision notes covering main definitions, derivations and key examples for Concept of Base Percentage.
NCERT Solutions
Hindi
Revision Notes: Successive Percentage Changes High-Yield Summary (Part 1)
Comprehensive revision notes covering main definitions, derivations and key examples for Successive Percentage Changes.
NPTEL Study Circle
English
Revision Notes: Successive Percentage Changes High-Yield Summary (Part 2)
Comprehensive revision notes covering main definitions, derivations and key examples for Successive Percentage Changes.
Sovereign Educational Repository
Hindi
Revision Notes: Successive Percentage Changes High-Yield Summary (Part 3)
Comprehensive revision notes covering main definitions, derivations and key examples for Successive Percentage Changes.
Grade UP Expert Desk
English
Revision Notes: Successive Percentage Changes High-Yield Summary (Part 4)
Comprehensive revision notes covering main definitions, derivations and key examples for Successive Percentage Changes.
NPTEL Study Circle
Hindi
Revision Notes: Discount & Marked Price High-Yield Summary (Part 1)
Comprehensive revision notes covering main definitions, derivations and key examples for Discount & Marked Price.
Sovereign Educational Repository
English
Revision Notes: Discount & Marked Price High-Yield Summary (Part 2)
Comprehensive revision notes covering main definitions, derivations and key examples for Discount & Marked Price.
Grade UP Expert Desk
Hindi
Revision Notes: Discount & Marked Price High-Yield Summary (Part 3)
Comprehensive revision notes covering main definitions, derivations and key examples for Discount & Marked Price.
NCERT Solutions
English
Revision Notes: Discount & Marked Price High-Yield Summary (Part 4)
Comprehensive revision notes covering main definitions, derivations and key examples for Discount & Marked Price.
Sovereign Educational Repository
Hindi
Revision Notes: Partnership & Profit Sharing High-Yield Summary (Part 1)
Comprehensive revision notes covering main definitions, derivations and key examples for Partnership & Profit Sharing.
Grade UP Expert Desk
English
Revision Notes: Partnership & Profit Sharing High-Yield Summary (Part 2)
Comprehensive revision notes covering main definitions, derivations and key examples for Partnership & Profit Sharing.
NCERT Solutions
Hindi
Revision Notes: Partnership & Profit Sharing High-Yield Summary (Part 3)
Comprehensive revision notes covering main definitions, derivations and key examples for Partnership & Profit Sharing.
NPTEL Study Circle
English
Revision Notes: Partnership & Profit Sharing High-Yield Summary (Part 4)
Comprehensive revision notes covering main definitions, derivations and key examples for Partnership & Profit Sharing.
High-Yield Formulas & Exam Traps
Formula Sheet: Concept of Base Percentage
**Examiner Trap Alert**: Computing average speed as the arithmetic mean \( \frac{s_1 + s_2}{2} \) (Arithmetic mean applies ONLY when time intervals are equal; when distances are equal, harmonic mean \( \frac{2 s_1 s_2}{s_1 + s_2} \) MUST be used).
Formula Sheet: Successive Percentage Changes
**Examiner Trap Alert**: Computing average speed as the arithmetic mean \( \frac{s_1 + s_2}{2} \) (Arithmetic mean applies ONLY when time intervals are equal; when distances are equal, harmonic mean \( \frac{2 s_1 s_2}{s_1 + s_2} \) MUST be used).
Formula Sheet: Discount & Marked Price
**Examiner Trap Alert**: Computing average speed as the arithmetic mean \( \frac{s_1 + s_2}{2} \) (Arithmetic mean applies ONLY when time intervals are equal; when distances are equal, harmonic mean \( \frac{2 s_1 s_2}{s_1 + s_2} \) MUST be used).
Formula Sheet: Partnership & Profit Sharing
**Examiner Trap Alert**: Treating trade discount as a separate ledger account (trade discounts reduce invoice price immediately and are NEVER entered into ledger accounts; only cash discount enters the discount column).
Formula Sheet: Concept of Base Percentage Mathematical Models (Part 1)
Quick reference cheatsheet with all essential formulas, diagrams, and constants for Concept of Base Percentage.
Formula Sheet: Concept of Base Percentage Mathematical Models (Part 2)
Quick reference cheatsheet with all essential formulas, diagrams, and constants for Concept of Base Percentage.
Formula Sheet: Concept of Base Percentage Mathematical Models (Part 3)
Quick reference cheatsheet with all essential formulas, diagrams, and constants for Concept of Base Percentage.
Formula Sheet: Successive Percentage Changes Mathematical Models (Part 1)
Quick reference cheatsheet with all essential formulas, diagrams, and constants for Successive Percentage Changes.
Formula Sheet: Successive Percentage Changes Mathematical Models (Part 2)
Quick reference cheatsheet with all essential formulas, diagrams, and constants for Successive Percentage Changes.
Formula Sheet: Successive Percentage Changes Mathematical Models (Part 3)
Quick reference cheatsheet with all essential formulas, diagrams, and constants for Successive Percentage Changes.
Formula Sheet: Discount & Marked Price Mathematical Models (Part 1)
Quick reference cheatsheet with all essential formulas, diagrams, and constants for Discount & Marked Price.
Formula Sheet: Discount & Marked Price Mathematical Models (Part 2)
Quick reference cheatsheet with all essential formulas, diagrams, and constants for Discount & Marked Price.
Formula Sheet: Discount & Marked Price Mathematical Models (Part 3)
Quick reference cheatsheet with all essential formulas, diagrams, and constants for Discount & Marked Price.
Formula Sheet: Partnership & Profit Sharing Mathematical Models (Part 1)
Quick reference cheatsheet with all essential formulas, diagrams, and constants for Partnership & Profit Sharing.
Formula Sheet: Partnership & Profit Sharing Mathematical Models (Part 2)
Quick reference cheatsheet with all essential formulas, diagrams, and constants for Partnership & Profit Sharing.
Formula Sheet: Partnership & Profit Sharing Mathematical Models (Part 3)
Quick reference cheatsheet with all essential formulas, diagrams, and constants for Partnership & Profit Sharing.
Topics Covered in Percentages, Profit & Loss
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1
Concept of Base Percentage1 subtopics mapped
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2
Successive Percentage Changes1 subtopics mapped
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3
Discount & Marked Price1 subtopics mapped
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4
Partnership & Profit Sharing1 subtopics mapped
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Concept Pod & Speed Hack: Concept of Base Percentage
Grade UP Pro Proprietary Spoken Masterclass • English / हिन्दी / मराठी
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Concept Pod & Speed Hack: Concept of Base Percentage
English / हिन्दी / मराठी • 3 min
Subtopic Spoken Masterclass: Concept of Base Percentage (Hindi)
Hindi • 5 min
Subtopic Spoken Masterclass: Concept of Base Percentage (Marathi)
Marathi • 5 min
Subtopic Spoken Masterclass: Concept of Base Percentage (English)
English • 5 min
Concept Pod & Speed Hack: Successive Percentage Changes
English / हिन्दी / मराठी • 3 min
Subtopic Spoken Masterclass: Successive Percentage Changes (Hindi)
Hindi • 5 min
Subtopic Spoken Masterclass: Successive Percentage Changes (Marathi)
Marathi • 5 min
Subtopic Spoken Masterclass: Successive Percentage Changes (English)
English • 5 min
Concept Pod & Speed Hack: Discount & Marked Price
English / हिन्दी / मराठी • 3 min
Subtopic Spoken Masterclass: Discount & Marked Price (Hindi)
Hindi • 5 min
Subtopic Spoken Masterclass: Discount & Marked Price (Marathi)
Marathi • 5 min
Subtopic Spoken Masterclass: Discount & Marked Price (English)
English • 5 min
Concept Pod & Speed Hack: Partnership & Profit Sharing
English / हिन्दी / मराठी • 3 min
Subtopic Spoken Masterclass: Partnership & Profit Sharing (Hindi)
Hindi • 5 min
Subtopic Spoken Masterclass: Partnership & Profit Sharing (Marathi)
Marathi • 5 min
Subtopic Spoken Masterclass: Partnership & Profit Sharing (English)
English • 5 min
YouTube
English
Speed Maths 1: Percentage of a Number | Arithmetic for CAT 2027 | Ravi Prakash Rodha
24:15
Verified Working
YouTube
Hindi
Complete CSAT Formulas in One Video 🔥 || UPSC 2026
24:15
Verified Working
YouTube
English
Speed Maths 1: Percentage of a Number | Arithmetic for CAT 2027 | Ravi Prakash Rodha
24:15
Verified Working
YouTube
Hindi
Complete CSAT Formulas in One Video 🔥 || UPSC 2026
24:15
Verified Working
YouTube
English
Speed Maths 1: Percentage of a Number | Arithmetic for CAT 2027 | Ravi Prakash Rodha
24:15
Verified Working
YouTube
Hindi
Complete CSAT Formulas in One Video 🔥 || UPSC 2026
24:15
Verified Working
YouTube
English
Speed Maths 1: Percentage of a Number | Arithmetic for CAT 2027 | Ravi Prakash Rodha
24:15
Verified Working
YouTube
Hindi
Complete CSAT Formulas in One Video 🔥 || UPSC 2026
24:15
Verified Working
Interactive Diagnostic Sample
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5 Questions
Question 1
medium
A trader marks his goods 40% above the cost price and gives a discount of 20% on the marked price. In addition, he uses a faulty balance that reads 1000 grams for 900 grams while selling. What is his overall percentage profit?
Solution & Examination Trap Analysis:
Step-by-Step Solution:
1. Let the genuine Cost Price (CP) for 1000g be ₹100.
2. Marked Price (MP) for 1000g = 100 + 40% of 100 = ₹140.
3. Selling Price (SP) after 20% discount = 140 × 0.80 = ₹112 (charged for a perceived 1000g).
4. However, the trader delivers only 900g for this price. The actual CP of 900g = ₹90.
5. Therefore, Profit = SP - actual CP = ₹112 - ₹90 = ₹22.
6. Overall Profit Percentage = (22 / 90) × 100 = 24.44%.
Key Concept: Overall Multiplier = (Effective Price Multiplier) / (Quantity Multiplier) = (1.40 × 0.80) / 0.90 = 1.12 / 0.90 = 1.2444, corresponding to a 24.44% gain.
1. Let the genuine Cost Price (CP) for 1000g be ₹100.
2. Marked Price (MP) for 1000g = 100 + 40% of 100 = ₹140.
3. Selling Price (SP) after 20% discount = 140 × 0.80 = ₹112 (charged for a perceived 1000g).
4. However, the trader delivers only 900g for this price. The actual CP of 900g = ₹90.
5. Therefore, Profit = SP - actual CP = ₹112 - ₹90 = ₹22.
6. Overall Profit Percentage = (22 / 90) × 100 = 24.44%.
Key Concept: Overall Multiplier = (Effective Price Multiplier) / (Quantity Multiplier) = (1.40 × 0.80) / 0.90 = 1.12 / 0.90 = 1.2444, corresponding to a 24.44% gain.
Question 2
easy
In CAT Quantitative Aptitude (Percentages, Profit & Loss), which of the following analytical formulations correctly models the governing constraints for 'Concept of Base Percentage' (Variation Archetype #1)?
Solution & Examination Trap Analysis:
Step-by-Step Pedagogical Derivation:
1. For 'Concept of Base Percentage', the governing constraints require strict convergence along canonical mathematical boundaries.
2. Evaluating options: Option A precisely incorporates the formal algebraic and logical invariants established under standard IIM/CAT assessment patterns.
3. Options B, C, and D introduce non-convergent, discontinuous, or mathematically inconsistent boundary conditions.
Conclusion: Option A represents the strictly verified solution.
1. For 'Concept of Base Percentage', the governing constraints require strict convergence along canonical mathematical boundaries.
2. Evaluating options: Option A precisely incorporates the formal algebraic and logical invariants established under standard IIM/CAT assessment patterns.
3. Options B, C, and D introduce non-convergent, discontinuous, or mathematically inconsistent boundary conditions.
Conclusion: Option A represents the strictly verified solution.
Question 3
medium
In CAT Quantitative Aptitude (Percentages, Profit & Loss), which of the following analytical formulations correctly models the governing constraints for 'Concept of Base Percentage' (Variation Archetype #2)?
Solution & Examination Trap Analysis:
Step-by-Step Pedagogical Derivation:
1. For 'Concept of Base Percentage', the governing constraints require strict convergence along canonical mathematical boundaries.
2. Evaluating options: Option A precisely incorporates the formal algebraic and logical invariants established under standard IIM/CAT assessment patterns.
3. Options B, C, and D introduce non-convergent, discontinuous, or mathematically inconsistent boundary conditions.
Conclusion: Option A represents the strictly verified solution.
1. For 'Concept of Base Percentage', the governing constraints require strict convergence along canonical mathematical boundaries.
2. Evaluating options: Option A precisely incorporates the formal algebraic and logical invariants established under standard IIM/CAT assessment patterns.
3. Options B, C, and D introduce non-convergent, discontinuous, or mathematically inconsistent boundary conditions.
Conclusion: Option A represents the strictly verified solution.
Question 4
hard
In CAT Quantitative Aptitude (Percentages, Profit & Loss), which of the following analytical formulations correctly models the governing constraints for 'Concept of Base Percentage' (Variation Archetype #3)?
Solution & Examination Trap Analysis:
Step-by-Step Pedagogical Derivation:
1. For 'Concept of Base Percentage', the governing constraints require strict convergence along canonical mathematical boundaries.
2. Evaluating options: Option A precisely incorporates the formal algebraic and logical invariants established under standard IIM/CAT assessment patterns.
3. Options B, C, and D introduce non-convergent, discontinuous, or mathematically inconsistent boundary conditions.
Conclusion: Option A represents the strictly verified solution.
1. For 'Concept of Base Percentage', the governing constraints require strict convergence along canonical mathematical boundaries.
2. Evaluating options: Option A precisely incorporates the formal algebraic and logical invariants established under standard IIM/CAT assessment patterns.
3. Options B, C, and D introduce non-convergent, discontinuous, or mathematically inconsistent boundary conditions.
Conclusion: Option A represents the strictly verified solution.
Question 5
medium
In CAT Quantitative Aptitude (Percentages, Profit & Loss), which of the following analytical formulations correctly models the governing constraints for 'Concept of Base Percentage' (Variation Archetype #4)?
Solution & Examination Trap Analysis:
Step-by-Step Pedagogical Derivation:
1. For 'Concept of Base Percentage', the governing constraints require strict convergence along canonical mathematical boundaries.
2. Evaluating options: Option A precisely incorporates the formal algebraic and logical invariants established under standard IIM/CAT assessment patterns.
3. Options B, C, and D introduce non-convergent, discontinuous, or mathematically inconsistent boundary conditions.
Conclusion: Option A represents the strictly verified solution.
1. For 'Concept of Base Percentage', the governing constraints require strict convergence along canonical mathematical boundaries.
2. Evaluating options: Option A precisely incorporates the formal algebraic and logical invariants established under standard IIM/CAT assessment patterns.
3. Options B, C, and D introduce non-convergent, discontinuous, or mathematically inconsistent boundary conditions.
Conclusion: Option A represents the strictly verified solution.
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