Quantitative Aptitude and Arithmetic

Why This Chapter Matters

Quantitative aptitude is often the section candidates fear most going in, and the section they regret under-practicing most looking back. The good news is that AP High Court and District Court staff exams draw from a fairly predictable pool of arithmetic topics — percentages, ratios, averages, simple and compound interest, time and work, time and distance, and basic profit-loss — and none of them require anything beyond Class 8–10 level mathematics. What separates a strong scorer from a weak one is not mathematical talent but familiarity with shortcuts and consistent practice with worked problems until the steps become automatic. This chapter walks through each core topic with full worked examples so you can build that automaticity.

Number System and Simplification

Before tackling application topics, be comfortable with basic number properties: LCM and HCF, divisibility rules, and simplification using BODMAS (Brackets, Orders/exponents, Division, Multiplication, Addition, Subtraction).

Worked Example: Simplify: 45 ÷ 9 × 3 + (12 − 4) × 2.

Step 1: Solve the bracket first: 12 − 4 = 8.

Step 2: Now the expression is 45 ÷ 9 × 3 + 8 × 2. Division and multiplication are done left to right: 45 ÷ 9 = 5, then 5 × 3 = 15. Also, 8 × 2 = 16.

Step 3: Now add: 15 + 16 = 31.

Step 4: Answer: 31.

Worked Example (LCM/HCF): The bells of a court complex ring at intervals of 12 minutes, 18 minutes, and 24 minutes respectively for shift changes. If all three ring together at 9:00 AM, when will they next ring together?

Step 1: This requires the LCM of 12, 18, and 24. Find prime factors: 12 = 2²×3, 18 = 2×3², 24 = 2³×3.

Step 2: LCM takes the highest power of each prime: 2³ × 3² = 8 × 9 = 72.

Step 3: All three will ring together again after 72 minutes, i.e., at 10:12 AM.

Percentages

Percentages are the backbone of most other arithmetic topics, so fluency here pays off across the whole section.

Worked Example: In a District Court recruitment exam, 8,000 candidates appeared. If 35% failed, how many candidates passed?

Step 1: If 35% failed, 65% passed (100% − 35% = 65%).

Step 2: Calculate 65% of 8,000: (65 ÷ 100) × 8000 = 65 × 80 = 5,200.

Step 3: Answer: 5,200 candidates passed.

Worked Example (Percentage change): The number of pending case files in a court office increased from 400 to 460 in one month. What is the percentage increase?

Step 1: Find the increase: 460 − 400 = 60.

Step 2: Percentage increase = (increase ÷ original) × 100 = (60 ÷ 400) × 100 = 15%.

Step 3: Answer: 15% increase.

Ratio and Proportion

Worked Example: The ratio of Junior Assistants to Typists in a court complex is 3:5. If there are 24 Junior Assistants, how many Typists are there?

Step 1: Set up the ratio as a fraction: 3/5 = 24/x, where x is the number of Typists.

Step 2: Cross-multiply: 3x = 5 × 24 = 120.

Step 3: Divide: x = 120 ÷ 3 = 40.

Step 4: Answer: 40 Typists.

Averages

Worked Example: The average age of 5 Process Servers in an office is 32 years. If a new Process Server aged 26 joins, what is the new average age?

Step 1: Total age of the original 5 = average × number = 32 × 5 = 160 years.

Step 2: Add the new person's age: 160 + 26 = 186 years, now across 6 people.

Step 3: New average = 186 ÷ 6 = 31 years.

Step 4: Answer: 31 years.

Simple Interest and Compound Interest

Simple Interest formula: SI = (Principal × Rate × Time) ÷ 100. Compound Interest formula: Amount = Principal × (1 + Rate/100)^Time, and CI = Amount − Principal.

Worked Example (SI): A clerk deposits ₹15,000 in a bank at 8% simple interest per annum for 3 years. Find the interest earned.

Step 1: Apply the formula: SI = (15000 × 8 × 3) ÷ 100.

Step 2: Calculate numerator: 15000 × 8 = 120,000; then 120,000 × 3 = 360,000.

Step 3: Divide by 100: 360,000 ÷ 100 = 3,600.

Step 4: Answer: ₹3,600 interest earned.

Worked Example (CI, 2 years, useful shortcut): Find the compound interest on ₹10,000 at 10% per annum for 2 years.

Step 1: For 2 years, a fast shortcut is: CI = P × [(R/100) × 2 + (R/100)²], or simply compute year by year.

Step 2: Year 1 interest: 10% of 10,000 = 1,000. New principal = 11,000.

Step 3: Year 2 interest: 10% of 11,000 = 1,100.

Step 4: Total CI = 1,000 + 1,100 = 2,100.

Step 5: Answer: ₹2,100.

Time and Work

Worked Example: A Record Assistant can sort a batch of files in 12 days, and a Junior Assistant can sort the same batch in 18 days. If they work together, how many days will they take?

Step 1: Find each person's one-day work rate: Record Assistant does 1/12 of the work per day; Junior Assistant does 1/18 per day.

Step 2: Combined rate per day = 1/12 + 1/18. Find common denominator (36): 3/36 + 2/36 = 5/36.

Step 3: Together they complete 5/36 of the work each day, so total days needed = 36/5 = 7.2 days.

Step 4: Answer: 7.2 days (or 7 days and about 4.8 hours).

Time, Speed, and Distance

Worked Example: A Process Server travels from the court office to deliver a summons 60 km away, traveling at 40 km/hr. He returns along the same route at 60 km/hr. Find his average speed for the entire trip.

Step 1: A common mistake is to simply average 40 and 60 to get 50 — this is incorrect when the distances covered at each speed are equal. Use the formula for average speed with equal distances: Average speed = (2 × Speed1 × Speed2) ÷ (Speed1 + Speed2).

Step 2: Substitute: (2 × 40 × 60) ÷ (40 + 60) = 4800 ÷ 100 = 48.

Step 3: Answer: 48 km/hr average speed.

Worked Example (basic): If a Typist travels 15 km in 30 minutes, what is her speed in km/hr?

Step 1: Convert 30 minutes to hours: 30/60 = 0.5 hours.

Step 2: Speed = distance ÷ time = 15 ÷ 0.5 = 30 km/hr.

Profit, Loss, and Discount

Worked Example: A stationery supplier buys registers at ₹80 each and sells them to a court office at ₹100 each. Find the profit percentage.

Step 1: Profit = Selling Price − Cost Price = 100 − 80 = 20.

Step 2: Profit percentage = (Profit ÷ Cost Price) × 100 = (20 ÷ 80) × 100 = 25%.

Step 3: Answer: 25% profit.

Common Exam Traps

• Averaging two speeds directly when distances are equal but times differ — always use the harmonic-mean-based formula (2×S1×S2)/(S1+S2) for equal-distance trips, not the simple arithmetic mean.
• Confusing percentage increase and percentage decrease base values — a 20% increase followed by a 20% decrease does NOT return to the original value, because the second percentage is calculated on a different (larger) base.
• In time and work problems, forgetting to convert individual work rates to a common denominator before adding fractions.
• Applying the simple interest formula when the question specifies compound interest, or vice versa — always check the keyword in the question before choosing a formula.
• In profit-loss questions, calculating profit percentage on the selling price instead of the cost price — profit and loss percentages are always calculated on cost price unless the question explicitly states otherwise.
• Losing time on unnecessarily long division instead of using approximation or elimination among answer choices when exact calculation is not required.

How to Revise This Chapter Efficiently

Quantitative aptitude rewards spaced, varied practice far more than reading formulas repeatedly. Keep one page per topic with just the core formula and one worked example, and revisit that page for two to three minutes daily rather than re-deriving everything from scratch each time. Time yourself on mixed problem sets weekly, since real exams interleave topics rather than grouping them, and the ability to quickly identify "this is a time-and-work problem" versus "this is a ratio problem" from the wording is itself a skill worth practicing. In your last ten days, prioritize the topics with the highest historical frequency in AP court staff papers — percentages, ratios, simple interest, time and work, and time and distance — since these four to five topics typically account for the bulk of the quantitative aptitude questions.