Ratio and Proportion Class 6 Worksheet — Free PDF Download with Answers

A ratio is a way of comparing two quantities of the same kind. When a recipe says "mix flour and sugar in the ratio $3:1$," it means for every $3$ parts flour, use $1$ part sugar. The ratio $3:1$ tells you the relative sizes, not the actual amounts.

A proportion is a statement that two ratios are equal: $\dfrac{a}{b} = \dfrac{c}{d}$, or equivalently $a : b :: c : d$. Proportions are the mathematical tool behind scaling — enlarging a photograph, converting currencies, calculating speed-distance-time problems, and dividing quantities fairly.

In Class 6, students learn to express ratios in simplest form, find equivalent ratios, test whether four numbers are in proportion, and solve word problems using the unitary method. These concepts are directly used in percentage, profit-loss, and speed-distance topics in Classes 7 and 8.

* Ratio — A comparison of two quantities $a$ and $b$ written as $a : b$ or $\dfrac{a}{b}$. Both quantities must be in the same unit.
* Simplest form — Divide both terms by their HCF. E.g., $12 : 18 = \dfrac{12}{6} : \dfrac{18}{6} = 2 : 3$.
* Equivalent ratios — Multiply or divide both terms by the same number. $2 : 3 = 4 : 6 = 6 : 9 = \ldots$
* Proportion — Four numbers $a, b, c, d$ are in proportion if $a : b = c : d$, i.e., $a \times d = b \times c$ (cross multiplication).
* Unitary method — Find the value for $1$ unit, then multiply for the required number of units. E.g., if $5$ books cost Rs. $150$, then $1$ book costs $\dfrac{150}{5} = 30$, so $8$ books cost $8 \times 30 = 240$.
* Dividing a quantity in a given ratio — To divide $S$ in the ratio $a : b$: first part $= \dfrac{a}{a+b} \times S$, second part $= \dfrac{b}{a+b} \times S$.
* Order matters — $3 : 5$ is not the same as $5 : 3$.

1. Print the PDF — Download from the links below.

2. Start with Level 1 (Easy) — 20 questions on expressing and simplifying ratios, and basic proportion checks.

3. Time yourself — 15 minutes for Level 1, 20 for Level 2, 25 for Level 3.

4. Check answers — Use the included answer key.

5. Revise mistakes — For word-problem errors, re-read the question and identify what "1 unit" represents.

6. Move to the next level — Progress when you score 16/20 or above.

Level 1 — Easy

1. Express the ratio $24 : 36$ in simplest form.
Solution: HCF of $24$ and $36$ is $12$. Simplest form $= 2 : 3$.

2. Are $4, 6, 8, 12$ in proportion?
Solution: Check cross products: $4 \times 12 = 48$ and $6 \times 8 = 48$. Yes, they are in proportion.

3. Express the ratio of $50$ cm to $2$ m in simplest form.
Solution: $2$ m $= 200$ cm. Ratio $= 50 : 200 = 1 : 4$.

Level 2 — Medium

1. If $7$ pens cost Rs. $105$, find the cost of $12$ pens.
Solution: Cost of $1$ pen $= \dfrac{105}{7} = 15$. Cost of $12$ pens $= 12 \times 15 =$ Rs. $180$.

2. Divide Rs. $560$ between A and B in the ratio $3 : 5$.
Solution: A's share $= \dfrac{3}{8} \times 560 =$ Rs. $210$. B's share $= \dfrac{5}{8} \times 560 =$ Rs. $350$.

3. The ratio of boys to girls in a class is $4 : 5$. If there are $20$ boys, how many girls are there?
Solution: $\dfrac{4}{5} = \dfrac{20}{x} \Rightarrow x = \dfrac{20 \times 5}{4} = 25$ girls.

Level 3 — Hard

1. A sum of Rs. $2{,}400$ is divided among P, Q, and R in the ratio $2 : 3 : 7$. Find each person's share.
Solution: Total parts $= 12$. P $= \frac{2}{12} \times 2400 =$ Rs. $400$. Q $= \frac{3}{12} \times 2400 =$ Rs. $600$. R $= \frac{7}{12} \times 2400 =$ Rs. $1{,}400$.

2. If $a : b = 3 : 4$ and $b : c = 5 : 6$, find $a : b : c$.
Solution: Make $b$ common: $a : b = 15 : 20$ and $b : c = 20 : 24$. So $a : b : c = 15 : 20 : 24$.

3. A car travels $240$ km on $15$ litres of fuel. How many litres are needed for $400$ km?
Solution: $1$ km uses $\frac{15}{240} = \frac{1}{16}$ litres. $400$ km uses $\frac{400}{16} = 25$ litres.

CBSE (NCERT — Ganita Prakash / Math Magic)
CBSE does not have a standalone "Ratio and Proportion" chapter at the Class 6 level in the latest Ganita Prakash edition, though the concept appears within other chapters. The previous NCERT textbook had a dedicated chapter. Students preparing for CBSE exams should still practise these concepts as they appear in word problems across chapters.

ICSE (Selina / ML Aggarwal)
ICSE has a dedicated "Ratio and Proportion" chapter at Class 6. It covers simplification, equivalent ratios, proportion, unitary method, and division of quantities. ICSE exams include multi-step word problems involving all these sub-topics.

IB MYP (Mathematics Framework)
The MYP covers ratios within the Number unit, connecting them to real-world contexts like map scales, recipe scaling, and currency conversion. Students are expected to explain their reasoning and apply proportional thinking to unfamiliar situations.

Key Differences:
* CBSE: Concepts distributed across chapters; less formal treatment at Class 6.
* ICSE: Dedicated chapter; comprehensive coverage with word problems.
* IB: Real-world applications; emphasis on proportional reasoning.

Download your free Ratio and Proportion worksheets:

* Ratio & Proportion ICSE Worksheet — 60 questions aligned to Selina / ML Aggarwal

Practise online:

* Practice Online — ICSE
* Practice Online — IB

Each worksheet has 20 questions per level with a detailed answer key.

* AI Maths Solver — Stuck on a proportion problem? Get a step-by-step solution.
* Spark Coach — AI tutor that guides with hints, not answers.
* Free Worksheets for All Classes — Worksheets from Class 1 to 10.
* Play Mode for Class 1-4 — Fun ratio games for younger learners.

Continue your Class 6 practice:

* Fractions & Decimals Class 6 Worksheet
* Numbers & Place Value Class 6 Worksheet
* Data Handling Class 6 Worksheet
* Prime Numbers & Factors Class 6 Worksheet
* Algebra & Simple Equations Class 6 Worksheet