Class 7 Ratio and Proportion Worksheet – Direct and Inverse Proportion

Master ratio and proportion with this worksheet for Class 7 with direct proportion, inverse proportion, compound ratios, and real-world applications. Includes solved examples and step-by-step methods to build problem-solving confidence.

What are Ratio and Proportion?

A ratio compares two quantities of the same kind. A proportion tells us that two ratios are equal. At Class 7, we go beyond basic ratios into direct and inverse proportion, compound ratios, and continued proportion. These concepts appear everywhere — from recipes and speed calculations to work problems and mixture questions. The key skill at this level is identifying which type of proportion applies before setting up the equation.

Key Concepts

Direct Proportion: When one quantity increases, the other increases at the same rate. Cost and quantity are directly proportional — double the quantity, double the cost.

Inverse Proportion: When one quantity increases, the other decreases. Workers and time are inversely proportional — more workers means less time to finish the same job. The relationship is captured by the formula: first quantity × second quantity = constant.

Compound Ratio: Found by multiplying two or more ratios together. The compound ratio of a:b and c:d is (a×c):(b×d).

Continued Proportion: Three numbers a, b, c are in continued proportion when a:b = b:c. This means b² = a×c, and b is called the mean proportional.

Solved Example

15 workers can build a wall in 12 days. How many workers are needed to finish the same wall in 9 days?

Step-by-Step Solution

First, identify the type of proportion. Fewer days means more workers are needed, so this is inverse proportion. For inverse proportion, the product stays constant: Workers × Days = constant.

Set up the equation: 15 × 12 = Workers × 9. This gives 180 = 9 × Workers. Dividing both sides by 9: Workers = 20.

Answer: 20 workers are needed to complete the wall in 9 days.

Practice Problems

• A car travels 240 km in 4 hours. At the same speed, how far will it travel in 6.5 hours? → Direct Proportion (Distance and Time)
• 20 men complete a job in 15 days. How many days will 25 men take? → Inverse Proportion (Workers and Time)
• The ratio of boys to girls in a school is 7:5. If there are 84 boys, find the number of girls and the total students. → Ratio Division
• A recipe for 4 people uses 300g flour and 200g sugar. Adjust the quantities for 10 people. → Scaling with Direct Proportion
• The monthly salaries of A and B are in the ratio 5:6. A gets a 20% raise and B gets 10%. Find the new ratio of their salaries. → Ratio After Percentage Change
• A car covers a distance in 8 hours at 60 km/h. At what speed must it travel to cover the same distance in 6 hours? → Inverse Proportion (Speed and Time)

Scoring Guide

• 20–24 marks: Excellent! Explore partnership problems, profit sharing, and mixture and alligation concepts.
• 15–19 marks: Very Good! Practice compound ratios and continued proportions. Master inverse proportion problems thoroughly.
• 10–14 marks: Good Effort! Focus on clearly understanding the difference between direct and inverse proportion. Practice the unitary method daily.
• 0–9 marks: Keep Trying! Go back to basic ratio concepts. Practice cross multiplication and work with real-life examples like cooking and shopping.

Tips and Common Mistakes

The most common error is confusing direct and inverse proportion. Ask yourself: if one quantity doubles, does the other double too or halve? If it doubles, it is direct. If it halves, it is inverse.

For inverse proportion, do not use the formula x₁/y₁ = x₂/y₂. Instead, use x₁ × y₁ = x₂ × y₂. Using the wrong formula gives the opposite answer.

Always simplify ratios to their lowest form. Writing 12:18 instead of 2:3 is incomplete and can cause confusion in further calculations.

When combining two ratios like a:b and b:c into a single ratio a:b:c, make the middle term equal in both ratios first. Skipping this step leads to wrong answers.

Order matters in a ratio. 3:5 is not the same as 5:3. Always keep track of which quantity comes first.

When combining ratios to form a compound ratio, multiply — do not add. The compound ratio of 2:3 and 4:5 is 8:15, not 6:8.