Ratio & proportion: Quantitative Aptitude Notes for Nagaland Forest Guard

📚 Ratio & Proportion – Quick & Easy Notes

(Perfect for the Nagaland Forest Guard’s Quantitative Aptitude prep)

1. What is a Ratio?

Definition: A ratio is a comparison of two numbers.
Format: A : B (read as “A to B”).
Everyday Analogy
- Think of a recipe that calls for 3 cups of sugar to 2 cups of flour.
- The recipe’s ratio is 3 : 2.

2. What is a Proportion?

Definition: Two ratios are equal → that’s a proportion.
Format: A : B = C : D
Everyday Analogy
- If you have 6 people and 12 chairs, the ratio of people to chairs is 6 : 12.
- If you now add 2 more people and 4 more chairs (keeping the same ratio), the new ratio is also 8 : 16.
- Since 6 : 12 = 8 : 16, the two ratios form a proportion.

3. Why Ratios & Proportions Matter

Mixing paints, fuels, or food.
Scaling maps or blueprints.
Comparing speeds, costs, or resources.

4. Quick Steps to Solve Ratio Problems

Write the ratio in simple form.
Set up the proportion if you need to find a missing number.
Cross‑multiply (multiply the opposite ends).
Solve for the unknown.
Check that the numbers make sense.

Tip: When numbers become huge, simplify the ratio first (divide by the greatest common divisor).

5. Tiny Example

Problem
A forest guard’s patrol uses 4 liters of diesel to cover 30 km.
If he needs to cover 45 km, how much diesel will he need?

Solution

Ratio of km to diesel: 30 km : 4 L → simplify → 15 km : 2 L.
Set up proportion:
30 km / 4 L = 45 km / x L
(or 15/2 = 45/x).
Cross‑multiply:
15 * x = 2 * 45 → 15x = 90.
Solve:
x = 90 / 15 = 6.

Answer: 6 liters of diesel.

6. Easy Practice Problems

#	Problem	Quick Hint
1	A forest ranger shares 5 apples with 3 friends. How many apples does each friend get?	Divide 5 by 3.
2	A map shows a scale of 1 cm : 20 km. What distance does 3 cm represent?	Multiply 3 by 20.
3	If 8 liters of ink fill 4 pages of a report, how many pages can 12 liters fill?	Set up proportion `8/4 = 12/x`.
4	A recipe that makes 12 cookies uses 3 cups of flour. How many cups are needed for 30 cookies?	Scale up by `30/12 = 2.5`.
5	6 patrol cars cover 90 km in a day. If 8 patrol cars work the same way, how many km will they cover?	Proportion `6/90 = 8/x`.

7. Quick Review Checklist

Can I write a ratio in the form A : B?
Do I know how to simplify a ratio?
Can I set up and solve a proportion using cross‑multiplication?
Do I check if the answer makes sense in context?

Final Thought

Think of a ratio like a “balance scale” that keeps two sides in proportion. When you keep the balance the same, you’re working with a proportion. Mastering this simple tool will help you solve many practical problems quickly—just like a forest guard who needs to make decisions fast on the field!