Quantitative Aptitude and Arithmetic for Forest Recruitment Exams

Why This Chapter Matters

Quantitative aptitude is the section where consistent, disciplined practice pays off more reliably than in almost any other part of the syllabus, because the underlying mathematics rarely changes — only the numbers in the question change. Forest recruitment exams draw their arithmetic questions from a well-defined set of topics: number system, simplification, percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time-speed-distance, and time and work. This chapter walks through each topic with the core formula, the reasoning behind it, and a fully worked example so you can see exactly how examiners phrase questions and exactly how to attack them under time pressure. Treat every formula here not as something to memorise blindly but as something to understand once and then drill until it becomes automatic.

Number System Basics

A strong footing in the number system saves time across the entire quantitative section because so many other topics quietly depend on it. Know your classifications cold: natural numbers, whole numbers, integers, rational and irrational numbers; know your divisibility rules (a number is divisible by 3 if the sum of its digits is divisible by 3; by 4 if its last two digits form a number divisible by 4; by 9 if the digit sum is divisible by 9); and be fluent with finding the LCM and HCF of two or more numbers using prime factorisation.

Worked Example: Find the HCF and LCM of 24 and 36.

• Step 1 — Prime factorise: 24 = 2³ × 3; 36 = 2² × 3².
• Step 2 — HCF takes the lowest power of each common prime: 2² × 3 = 12.
• Step 3 — LCM takes the highest power of each prime appearing in either number: 2³ × 3² = 8 × 9 = 72.
• Answer: HCF = 12, LCM = 72. (Quick check: HCF × LCM should equal the product of the two numbers — 12 × 72 = 864, and 24 × 36 = 864, confirming the answer.)

Simplification and BODMAS

Simplification questions test whether you correctly apply the order of operations: Brackets, Of, Division, Multiplication, Addition, Subtraction. The most common source of error is not knowing BODMAS itself but rushing through a long expression and skipping a step, so always simplify the innermost bracket first and work outward, and always complete every division and multiplication (left to right) before moving to addition and subtraction (left to right).

Worked Example: Simplify: 24 ÷ 4 × (3 + 2) − 6.

• Step 1 — Brackets first: (3 + 2) = 5. Expression becomes 24 ÷ 4 × 5 − 6.
• Step 2 — Division and multiplication, left to right: 24 ÷ 4 = 6, then 6 × 5 = 30.
• Step 3 — Subtraction: 30 − 6 = 24.
• Answer: 24.

Percentages

A percentage is simply a fraction with denominator 100, and nearly every percentage question can be solved faster by converting the percentage to a fraction than by working with decimals. Learn the standard conversions by heart: 50% = 1/2, 25% = 1/4, 20% = 1/5, 12.5% = 1/8, 10% = 1/10, 33⅓% = 1/3 — recognising these instantly turns many percentage calculations into simple fraction arithmetic you can do without a calculator.

Worked Example: In a forest survey of 2,400 saplings, 15% were found damaged by pests. How many saplings were undamaged?

• Step 1 — Damaged saplings = 15% of 2,400 = (15/100) × 2,400 = 360.
• Step 2 — Undamaged saplings = 2,400 − 360 = 2,040.
• Answer: 2,040 saplings.

Ratio and Proportion

A ratio compares two quantities of the same kind, and a proportion states that two ratios are equal. The key skill is converting word problems into ratio form correctly and then scaling the ratio using a single common multiplier, often called "parts."

Worked Example: The ratio of male to female staff in a forest range office is 5:3. If there are 24 female staff, how many male staff are there, and what is the total staff strength?

• Step 1 — The ratio 5:3 means for every 3 parts female, there are 5 parts male. Since 3 parts = 24, one part = 8.
• Step 2 — Male staff = 5 parts = 5 × 8 = 40.
• Step 3 — Total staff = 5 parts + 3 parts = 8 parts = 8 × 8 = 64.
• Answer: 40 male staff, 64 total staff.

Averages

Average equals the sum of all values divided by the number of values. The most useful shortcut for averages questions is the deviation method: instead of adding all the numbers, pick a convenient reference value close to the numbers, find how far each number deviates above or below that reference, sum the deviations, and adjust the reference by the average deviation.

Worked Example: The average height of 6 tree saplings is 1.5 metres. A seventh sapling of height 2.2 metres is added. Find the new average.

• Step 1 — Total height of original 6 saplings = 6 × 1.5 = 9 metres.
• Step 2 — New total = 9 + 2.2 = 11.2 metres, across 7 saplings.
• Step 3 — New average = 11.2 / 7 = 1.6 metres.
• Answer: 1.6 metres.

Profit and Loss

Profit or loss is always calculated on the cost price (CP), never on the selling price (SP), unless a question explicitly states otherwise — this is the single most important rule in this topic. Profit = SP − CP; Loss = CP − SP; Profit% = (Profit/CP) × 100; Loss% = (Loss/CP) × 100.

Worked Example: A forest nursery bought seedlings at ₹40 each and sold them at ₹52 each. Find the profit percentage.

• Step 1 — Profit per seedling = 52 − 40 = 12.
• Step 2 — Profit% = (12/40) × 100 = 30%.
• Answer: 30% profit.

Simple Interest and Compound Interest

Simple Interest (SI) = (Principal × Rate × Time) / 100. Compound Interest (CI) is calculated on the accumulating amount rather than a fixed principal, and the compound amount formula is A = P(1 + R/100)^T, with CI = A − P. The key exam distinction is that SI is the same amount every year, while CI grows larger each year because interest is earned on previously earned interest as well.

Worked Example: Find the compound interest on ₹10,000 for 2 years at 10% per annum, compounded annually.

• Step 1 — Amount after year 1 = 10,000 × 1.10 = 11,000.
• Step 2 — Amount after year 2 = 11,000 × 1.10 = 12,100.
• Step 3 — CI = 12,100 − 10,000 = 2,100.
• Answer: ₹2,100.

Time, Speed, and Distance

The core relationship is Distance = Speed × Time, and every question in this topic is a variation on rearranging this one formula. Remember the conversion: to convert km/h to m/s, multiply by 5/18; to convert m/s to km/h, multiply by 18/5. For problems involving two moving bodies, remember that relative speed is the sum of their speeds when moving toward each other or in opposite directions, and the difference of their speeds when moving in the same direction.

Worked Example: A forest patrol jeep travels at 60 km/h. How long does it take to cover 150 km?

• Step 1 — Time = Distance / Speed = 150 / 60 = 2.5 hours.
• Answer: 2.5 hours, or 2 hours 30 minutes.

Worked Example (relative speed): Two patrol teams start 100 km apart and walk toward each other at 6 km/h and 4 km/h respectively. After how many hours will they meet?

• Step 1 — Relative speed (moving toward each other) = 6 + 4 = 10 km/h.
• Step 2 — Time to meet = Total distance / Relative speed = 100 / 10 = 10 hours.
• Answer: 10 hours.

Time and Work

The standard approach is to convert each worker's time-to-complete into a work rate, expressed as "the fraction of the job done in one day," and then add rates when people work together. If a person can finish a job in N days, their one-day work rate is 1/N.

Worked Example: A can plant a nursery bed in 12 days, and B can plant the same bed in 18 days. In how many days will they finish it working together?

• Step 1 — A's one-day work = 1/12; B's one-day work = 1/18.
• Step 2 — Combined one-day work = 1/12 + 1/18. LCM of 12 and 18 is 36, so this is 3/36 + 2/36 = 5/36.
• Step 3 — Days to finish together = 36/5 = 7.2 days.
• Answer: 7.2 days, or 7 days and about 4.8 hours.

Common Exam Traps

• Calculating profit or loss percentage on the selling price instead of the cost price.
• Forgetting to convert km/h to m/s (or vice versa) before combining values in a time-speed-distance problem.
• Adding speeds for two bodies moving in the same direction instead of subtracting them, or vice versa for opposite directions.
• Applying the simple interest formula when the question clearly says "compounded annually," producing an answer that looks reasonable but is wrong.
• In averages problems, forgetting to divide by the new, larger count after adding or removing a value.
• Rushing through BODMAS and performing addition before finishing all multiplication and division in a long expression.
• Setting up a ratio in the wrong order (reversing which quantity corresponds to which number in the ratio).
• In time and work problems, adding the number of days directly instead of adding the work rates (fractions).

How to Revise This Chapter Efficiently

Build a single reference sheet with just the nine formulas from this chapter, written in your own words, and keep it beside you during every practice session until you no longer need to check it. Quantitative aptitude improves through volume of varied practice more than through re-reading theory, so aim to solve at least twenty to thirty mixed questions across these nine topics every day in the final month, always under a timer, and always writing down which formula you used before you start calculating — this habit alone prevents most of the traps listed above.