Quantitative Aptitude — Banking Exam Notes

Topics Covered

1. Number System 2. Percentage 3. Profit & Loss 4. SI & CI 5. Ratio & Proportion 6. Time & Work 7. Speed & Distance 8. Data Interpretation 9. Quadratic Equations 10. Simplification

Number System

Types of Numbers

Natural Numbers: 1, 2, 3 ... (counting numbers, no zero)

Whole Numbers: 0, 1, 2, 3 ... (natural + zero)

Integers: ...-3, -2, -1, 0, 1, 2, 3...

Rational Numbers: Numbers expressible as p/q where q ≠ 0

Prime Numbers: Divisible only by 1 and itself (2, 3, 5, 7, 11...)

Key Formulas

Divisibility Rules:
• By 2: last digit even • By 3: sum of digits divisible by 3
• By 4: last 2 digits divisible by 4 • By 9: digit sum divisible by 9
• By 11: (odd position sum) - (even position sum) = 0 or multiple of 11

Exam Tip

LCM × HCF = Product of two numbers. If asked for LCM of fractions: LCM = LCM(numerators) / HCF(denominators). HCF of fractions = HCF(numerators) / LCM(denominators).

Percentage

Core Concepts

Percent means “per hundred”. x% of y = (x/100) × y

Important Formulas

• % increase = (Increase/Original) × 100
• % decrease = (Decrease/Original) × 100
• If A is x% more than B: B is [x/(100+x)] × 100 % less than A
• Successive % change: a% then b% = a + b + ab/100 (net % change)

Fraction	Decimal	Percentage
1/2	0.5	50%
1/3	0.333	33.33%
1/4	0.25	25%
1/5	0.2	20%
1/8	0.125	12.5%

Profit & Loss

Formulas

• Profit = SP - CP • Loss = CP - SP
• Profit% = (Profit/CP) × 100 • Loss% = (Loss/CP) × 100
• SP = CP × (100 + P%)/100 • CP = SP × 100/(100 + P%)

High-Frequency Type

Dishonest shopkeeper uses false weight: Gain% = (Error/(True value - Error)) × 100. Also, if articles are bought at x for Rs. A and sold at y for Rs. B: Profit% = (Bx - Ay)/(Ay) × 100.

Simple & Compound Interest

Core Formulas

SI = PRT/100 Amount (SI) = P + PRT/100
CI = P[(1 + R/100)^n - 1] Amount (CI) = P(1 + R/100)^n
Difference (CI-SI) for 2 years = P(R/100)²

Speed Trick

For 2 years: CI is always greater than SI. Difference = P × (R/100)². For 3 years: Difference = P(R/100)²(3 + R/100). Memorise these to save calculation time.

Ratio, Proportion & Mixture

Key Rules

• If A:B = m:n and B:C = p:q, then A:C = mp:nq
• Alligation: (Cheaper quantity)/(Costlier quantity) = (CP of costlier - Mean price)/(Mean price - CP of cheaper)
• Mixture problems: Use alligation rule for fast solving

Time & Work / Pipes & Cisterns

Formulas

• If A does work in ‘a’ days: A’s 1-day work = 1/a
• A + B together: 1 day work = 1/a + 1/b; Days = ab/(a+b)
• Pipe filling: same as work. Pipe draining: subtract instead of add.
• Efficiency ratio inversely proportional to time.

Banking Exam Favourite

LCM method: Find LCM of all given days. This LCM is the “total work.” Divide by individual days to get efficiency. Much faster than fraction method.

Speed, Distance & Time / Trains & Boats

Core

Speed = Distance/Time Distance = Speed × Time
Trains: Time = (Length of train + Length of platform)/Speed
Boats: Downstream speed = B + W; Upstream = B - W
Speed in still water = (D + U)/2; Current speed = (D - U)/2

Data Interpretation

DI comprises 15-20 marks in mains exams. Types: Bar Graph, Line Graph, Pie Chart, Table, Caselet, Mixed DI.

DI Strategy

• Read all 5 questions before starting calculations — some may share calculation steps.
• Approximate wherever possible: 48% ≈ 50%, 33% ≈ 1/3rd, 67% ≈ 2/3rd.
• In pie charts, always check if data is in % or absolute values.
• Caselet DI: Extract all numbers into a table before solving.

DI Type	What to look for	Common operations
Bar Graph	Height differences, comparisons	%, ratio, absolute difference
Line Graph	Trend, steepest rise/fall	Growth rate, % change
Pie Chart	Degree or %, total given	Value = (Degree/360) × Total
Table	Rows and columns carefully	Row totals, averages
Caselet	Conditions in paragraph	Equation formation

Quadratic Equations

Format: ax² + bx + c = 0. Find roots and compare x and y.

Methods

Factorisation: Find two numbers whose product = ac and sum = b.
Formula: x = [-b ± √(b²-4ac)] / 2a
Comparing roots: x > y, x < y, x ≥ y, x ≤ y, or cannot be determined.

Speed Method

For x² - 5x + 6 = 0: find two numbers = 5 (sum) and 6 (product). That’s 2 and 3. So x = 2 or 3. Never use the quadratic formula in exam — factorisation is always faster for banking-style questions.

Simplification & Approximation

BODMAS Rule

Bracket → Orders (powers, roots) → Division → Multiplication → Addition → Subtraction

Square & Cube Roots to Memorise

√2=1.414, √3=1.732, √5=2.236, √6=2.449, √7=2.646
Squares: 11²=121, 12²=144, 13²=169, 14²=196, 15²=225, 16²=256, 17²=289, 18²=324, 19²=361, 20²=400, 25²=625

Approximation Rule

Round to nearest 5 or 10 for quick calculation. Only approximate when the question says “approximate value” or “nearest to.” In simplification questions, find exact value — do not approximate.