Basic Mathematics — Module Overview
Mathematics appears only in the 5-Year LLB paper with 8 questions at Class 10 level (Maharashtra Board). This is the most scoring section per time invested — 8 marks in just ~10 minutes if you practice the key formulas!
The topics are straightforward and predictable. With focused preparation using this module, you can reliably score 6–8 out of 8 marks.
Topic-wise Breakdown
Exam Strategy for Mathematics (5-Year LLB)
Profit & Loss · Percentage
This is the highest-weightage topic — expect 2–3 questions. Master these formulas and you've guaranteed yourself 2 easy marks every paper.
Core Formulas — Profit & Loss
Core Formulas — Percentage & Average
Q. A shopkeeper bought a shirt for ₹500 and sold it for ₹650. Find the profit percentage.
Step 1: Profit = SP − CP = 650 − 500 = ₹150
Step 2: Profit % = (150 / 500) × 100 = 30%
✅ Answer: 30% — This is a classic Type-1 question. Direct formula application.
Q. A book is sold at ₹240, gaining 20% profit. What was the Cost Price?
Step: CP = SP × 100 / (100 + Profit%) = 240 × 100 / 120 = ₹200
✅ Answer: ₹200 — Remember: when profit% is given and you need CP, divide by (100 + P%).
Q. A TV has a Marked Price of ₹15,000 and is sold at 15% discount. Find the Selling Price.
Step: Discount = 15% of 15,000 = ₹2,250 → SP = 15,000 − 2,250 = ₹12,750
✅ Answer: ₹12,750 — Shortcut: SP = MP × (100 − D%) / 100 = 15000 × 85/100 = ₹12,750
- If an item is sold at x% profit and y% loss on two identical items → Net effect = (x − y − xy/100)%
- If two items sold at same SP with x% profit and x% loss → Always a net loss of (x²/100)%
- Successive Discount of a% & b% = Single discount of (a + b − ab/100)%
- Dishonest shopkeeper using false weight → Gain% = [(True Weight − False Weight) / False Weight] × 100
Simple Interest & Compound Interest
SI & CI contribute 1–2 questions per paper. The formulas are fixed — memorize them once and you'll always get these marks.
Simple Interest (SI)
Compound Interest (CI)
Q. ₹5,000 is invested at 8% per annum for 3 years. Find SI and Total Amount.
SI = (5000 × 8 × 3) / 100 = ₹1,200
Amount = 5000 + 1200 = ₹6,200
Q. ₹10,000 invested at 10% p.a. compound interest for 2 years. Find CI.
A = 10,000 × (1.1)² = 10,000 × 1.21 = ₹12,100
CI = 12,100 − 10,000 = ₹2,100
Quick check: SI for 2 years = ₹2,000. CI > SI ✅. Difference = ₹100 = P × (R/100)² = 10000 × 0.01 ✅
Speed, Distance & Time
A consistent source of 1–2 questions. The golden triangle formula applies to almost every variant of this question type.
The Golden Triangle Formula
Relative Speed — Key Rules
- Same direction: Relative Speed = S₁ − S₂ (subtract speeds)
- Opposite direction: Relative Speed = S₁ + S₂ (add speeds)
- Train crossing a pole/person: Distance = Length of Train
- Train crossing a platform: Distance = Length of Train + Length of Platform
- Two trains crossing each other: Distance = Sum of their lengths; Relative Speed = Sum (opposite) or Difference (same direction)
Q. A 200 m long train runs at 72 km/h. In how many seconds will it cross a 100 m platform?
Step 1: Convert speed → 72 km/h = 72 × 5/18 = 20 m/s
Step 2: Total distance = 200 + 100 = 300 m
Step 3: Time = 300 / 20 = 15 seconds
Q. A car travels from A to B at 60 km/h and returns at 40 km/h. Find average speed.
Average Speed = 2 × 60 × 40 / (60 + 40) = 4800 / 100 = 48 km/h
Note: Average speed ≠ arithmetic mean (60+40)/2 = 50. The harmonic mean formula must be used when same distance at two speeds.
Algebra — Basic Equations
Algebra questions test linear equations, basic identities, and word-problem translation. Class 9–10 level; no quadratic formula required in the exam.
Key Algebraic Identities
Solving Linear Equations — Steps
- Step 1: Translate the word problem into an equation. Assign a variable (x) to the unknown.
- Step 2: Collect like terms on both sides of the equation.
- Step 3: Isolate the variable by performing inverse operations.
- Step 4: Verify by substituting the value back into the original equation.
Q. The sum of ages of A and B is 45 years. If A is 5 years older than B, find their ages.
Let B's age = x, then A's age = x + 5
Equation: x + (x + 5) = 45 → 2x = 40 → x = 20
✅ B = 20 years, A = 25 years. Verify: 20 + 25 = 45 ✓
Q. If 2x + y = 7 and x + 2y = 8, find x and y.
Multiply eq. 1 by 2: 4x + 2y = 14
Subtract eq. 2: 3x = 6 → x = 2
Substitute: 2(2) + y = 7 → y = 3
- Age Problems: "A is twice as old as B…", "ratio of ages 3:5…"
- Number Problems: "Sum of two numbers is 50, difference is 10…"
- Mixture Problems: "Mix 20L of 30% solution with 30L of 20% solution…"
- Work Problems: "A can do a work in 6 days, B in 9 days. Together…" → Combined rate = 1/6 + 1/9
Venn Diagrams & Set Theory
1 question reliably from Set Theory. The n(A∪B) formula is all you need for MHT CET. Practice reading Venn diagram diagrams and translating the word problem into set notation.
Core Set Theory Formulas
Set Notation Glossary
Q. In a group of 100 students, 60 like cricket, 45 like football, and 25 like both. How many like at least one sport?
n(A∪B) = n(A) + n(B) − n(A∩B) = 60 + 45 − 25 = 80 students
How many like neither? = 100 − 80 = 20 students
How many like only cricket? = 60 − 25 = 35 students
How many like only football? = 45 − 25 = 20 students
Formula Flashcards
Click each card to reveal the formula or answer. Review all 12 cards to mark your progress. ✅ Cards turn green when reviewed.
Always on Cost Price (CP), never on SP!
Discount % = (Discount / MP) × 100
SP = MP × (100 − D%) / 100
P = Principal, R = Rate%, T = Time in years
CI = A − P
For 2 years: CI > SI; Diff = P(R/100)²
NOT (a+b)/2 — common mistake!
This is the Harmonic Mean formula.
km/h → m/s: × 5/18
m/s → km/h: × 18/5
e.g., 72 km/h = 72 × 5/18 = 20 m/s
"At least one" = n(A∪B)
Neither = n(U) − n(A∪B)
(a − b)² = a² − 2ab + b²
(a + b)(a − b) = a² − b²
Loss % = x²/100
e.g., 10% profit + 10% loss → 1% net loss
% Decrease = (Decrease / Original) × 100
Original = New Value for reversal problems
Opposite direction → S₁ + S₂ (add)
Train crossing platform: D = L(train) + L(platform)
Combined rate = sum of individual rates
Practice Quiz — 8 Questions
MHT CET LAW style questions at exact difficulty. Select an answer to see instant explanation. Score 6/8 or above = Exam-Ready! 🏆
Profit = 1000 − 800 = ₹200. Profit % = (200/800) × 100 = 25%. Remember: always on CP!
SI = (P × R × T) / 100 = (6000 × 5 × 4) / 100 = 120000/100 = ₹1,200
Speed = 180/3 = 60 km/h. Convert: 60 × 5/18 = 300/18 ≈ 16.67 m/s
n(A∪B) = 120 + 90 − 40 = 170. Neither = 200 − 170 = 30.
a² + b² = (a+b)² − 2ab = 100 − 42 = 58. (a−b)² = a²+b²−2ab = 58 − 42 = 16. a−b = 4.
A = 5000 × (1.1)² = 5000 × 1.21 = ₹6,050. CI = 6050 − 5000 = ₹1,050. (SI would be ₹1,000; CI > SI by ₹50 = 5000×(0.1)² = ₹50 ✓)
Let x + y = 50, x − y = 14. Adding: 2x = 64, x = 32. Verify: 32 − y = 14, y = 18. Sum = 32+18 = 50 ✓
Let CP = 100. MP = 140 (40% markup). SP = 140 × 80/100 = 112 (20% discount). Profit = 112−100 = 12. Profit% = 12%.