Ratio & proportion: Quantitative Aptitude Notes for Goa Police Constable

Ratio & Proportion – Quick Study Notes

(For Goa Police Constable – Quantitative Aptitude)

Ratio is a comparison of two numbers.
Think of it as “how many of A for every B.”
Example: If there are 4 boys and 6 girls in a class, the ratio of boys to girls is 4 : 6 (read as “4 to 6”).

Everyday analogy

Imagine you have 4 red marbles and 6 blue marbles.
You can say “for every 4 red marbles, there are 6 blue marbles.” That is the ratio.

A proportion is an equation that says two ratios are equal.
Written as a : b = c : d or a/b = c/d.
It tells us that the relationship between a and b is the same as that between c and d.

Everyday analogy

Suppose a recipe needs 2 cups of flour for every 3 cups of sugar.
If you want the same taste but use 4 cups of flour, you need 6 cups of sugar – the two ratios 2:3 and 4:6 are in proportion.

Step	What to do	Quick tip
1	Write the ratio in the form `x : y`.	Use a colon `:`.
2	Simplify if needed (divide both by their greatest common divisor).	Keeps numbers small.
3	Find the common “part” if you need a total amount.	`part = total ÷ (x + y)`.
4	Multiply the part by each side to get the individual amounts.	`value of x = part × x`, `value of y = part × y`.

Total of apples and oranges = 20
Ratio apples : oranges = 3 : 5

(If you need whole numbers, adjust the total so the part becomes an integer.)

Step	What to do	Quick tip
1	Set up the proportion: `a : b = c : d`.	Write it as `a/b = c/d`.
2	Cross‑multiply (multiply diagonally): `a × d = b × c`.	Think “cross” and “multiply”.
3	Solve for the unknown (usually `c` or `d`).	Isolate the variable on one side.

If 5 pens cost Rs 25, how much do 8 pens cost?

Problem Type	How to Approach
“In” ratios (`x in y`)	Treat `x` as part of the whole; use `part = y ÷ (x + remaining parts)`.
“As” ratios (`x as y`)	Same as “in”; often used when comparing two situations.
Scaling up/down	Multiply or divide both numbers by the same factor.
Finding a missing part	Set up a proportion and cross‑multiply.

Read carefully – “for every” or “in” tells you which numbers go together.
Keep numbers small – simplify ratios before starting calculations.
Check units – if the answer should be in rupees, keep track of the currency symbol.
Use cross‑multiplication – it is faster than converting to decimals.
Double‑check – plug the answer back into the original ratio to confirm.

Ratio
There are 7 boys and 9 girls in a class.
What is the ratio of boys to girls?

Answer: 7 : 9
Proportion (find missing value)
12 : 18 = 3 : x
Find x.

Solution: 12 × x = 18 × 3 → 12x = 54 → x = 54 ÷ 12 = 4.5
Total amount from ratio
If a recipe uses 4 cups of flour for every 6 cups of sugar and you need a total of 20 cups of dry mix, how many cups of sugar are needed?

Solution:
- Part