Arithmetic – Study Notes for SBI Clerk Prelims
Overview
Arithmetic forms the backbone of the Numerical Ability section in SBI Clerk Prelims. These questions test your ability to apply basic mathematical concepts quickly—speed matters more than complexity at the Clerk level.
The good news: SBI Clerk Prelims arithmetic stays at a moderate difficulty level. Questions are direct applications of formulas with 1–2 step calculations. If you master the core formulas and practice mental math shortcuts, you can solve most arithmetic questions in under 60 seconds each. This section rewards preparation—patterns repeat, and the same question types appear year after year.
Focus areas in order of importance: Percentage, Ratio & Proportion, Profit & Loss, Simple & Compound Interest, Time & Work, and Time-Speed-Distance. Problems on Ages and Partnership appear less frequently but are easy marks when they do appear.
Key Concepts
- Percentage is the foundation: Almost every arithmetic topic—profit/loss, interest, ratio changes—ultimately converts to percentage calculations. Master percentage first.
- Ratio thinking beats equation solving: Instead of setting up algebraic equations, think in terms of "parts" and "multipliers." A 3:5 ratio means 8 total parts—this mental model speeds up calculations.
- Work and Time are inversely proportional: If A is twice as efficient as B, A takes half the time. This inverse relationship applies to pipes/cisterns too.
- SI grows linearly, CI grows exponentially: Simple Interest adds the same amount each year. Compound Interest adds increasing amounts because interest earns interest.
- CP-SP-MP form a triangle: Cost Price → add profit margin → Selling Price. Marked Price → subtract discount → Selling Price. Most problems ask you to navigate this triangle.
- Relative speed determines meeting/crossing problems: Same direction = subtract speeds. Opposite direction = add speeds. This single rule covers trains, boats, and all motion problems.
- Mixture problems are weighted averages: Alligation is just a shortcut for finding the ratio in which two quantities at different values must be mixed to get a target value.
- Age problems create linear equations: The key insight—age differences stay constant. If A is 5 years older than B today, A will always be 5 years older.
Formulas / Key Facts
Percentage
- x% of y = y% of x = (xy)/100
- Percentage change = (Change / Original) × 100
- If a value increases by R%, new value = Original × (1 + R/100)
- Successive % changes: Net effect ≠ sum of percentages. Use: a + b + (ab/100)
Ratio and Proportion
- If a:b = c:d, then ad = bc (cross multiplication)
- Componendo: (a+b)/b = (c+d)/d
- If ratio is a:b and total is T, parts are aT/(a+b) and bT/(a+b)
Profit and Loss
- Profit% = (Profit/CP) × 100
- SP = CP × (100 + Profit%)/100
- Discount% = (Discount/MP) × 100
- SP = MP × (100 − Discount%)/100
Simple Interest
- SI = (P × R × T)/100
- Amount = P + SI
Compound Interest
- Amount = P × (1 + R/100)^T
- CI = Amount − P
- For 2 years: CI − SI = P × (R/100)²
Time and Work
- If A does work in 'a' days, A's 1 day work = 1/a
- Combined work: 1/a + 1/b = 1/T (T = time together)
- Efficiency ratio = Inverse of time ratio
Time, Speed and Distance
- Distance = Speed × Time
- Average speed (same distance) = 2ab/(a+b) where a, b are speeds
- Relative speed: Same direction = |a−b|, Opposite = a+b
Mixture and Alligation
- Alligation rule: Ratio = (Higher value − Mean) : (Mean − Lower value)
Partnership
- Profit share ∝ Capital × Time
Problems on Ages
- Present age problems: Let present ages be x and y, form equations from given conditions
Worked Examples
Example 1: Profit and Loss A shopkeeper marks goods 25% above CP and gives 10% discount. Find profit%.
Solution: Let CP = 100 MP = 100 + 25% of 100 = 125 Discount = 10% of 125 = 12.5 SP = 125 − 12.5 = 112.5 Profit = 112.5 − 100 = 12.5 Profit% = (12.5/100) × 100 = 12.5%
Example 2: Time and Work A can complete work in 12 days, B in 18 days. They work together for 4 days, then A leaves. How many more days will B take to finish?
Solution: A's 1 day work = 1/12, B's 1 day work = 1/18 Together in 1 day = 1/12 + 1/18 = 5/36 Work done in 4 days = 4 × 5/36 = 20/36 = 5/9 Remaining work = 1 − 5/9 = 4/9 Days for B to finish = (4/9) ÷ (1/18) = (4/9) × 18 = 8 days
Example 3: SI vs CI Find the difference between CI and SI on Rs 8000 at 5% for 2 years.
Solution: CI − SI for 2 years = P × (R/100)² = 8000 × (5/100)² = 8000 × 1/400 = Rs 20
Common Mistakes
- Adding successive percentages directly → Wrong: 10% increase then 20% increase ≠ 30% increase. Correct: Use formula a + b + ab/100 = 10 + 20 + 200/100 = 32%.
- Calculating profit% on SP instead of CP → Wrong thinking: "I sold for 120 and made 20 profit, so profit% = 20/120." Correct: Always calculate profit% on CP, so it's 20/100 = 20%.
- Confusing time taken with work done → Wrong: If A is twice as fast, A takes twice the time. Correct: A takes half the time (inverse relationship).
- Using wrong base for discount → Wrong: Discount% calculated on CP. Correct: Discount is always calculated on Marked Price.
- Forgetting units in speed problems → Mixing km/hr and m/s without conversion. Correct: km/hr × 5/18 = m/s.
Quick Reference
- Successive % changes: Net = a + b + (ab/100)
- Profit% = (SP − CP)/CP × 100; Discount% = (MP − SP)/MP × 100
- CI − SI for 2 years = P(R/100)²
- Combined work rate = Sum of individual rates
- Average speed for equal distances = 2ab/(a+b)
- Alligation ratio = (Expensive − Mean) : (Mean − Cheap)