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Ratio and Proportion - Solving problems involving direct proportion

Grade 5IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Direct Proportion: Two quantities are in direct proportion if, as one quantity increases, the other increases at the same rate.

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Constant Ratio: In direct proportion, the ratio between the two quantities always remains the same.

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The Unitary Method: A technique where you first find the value of a single unit (one item) before finding the value of the required number of units.

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Scaling: You can multiply or divide both quantities in a proportion by the same number to maintain the balance.

📐Formulae

Unit Value=Total ValueNumber of Units\text{Unit Value} = \frac{\text{Total Value}}{\text{Number of Units}}

Total Value=Unit Value×New Number of Units\text{Total Value} = \text{Unit Value} \times \text{New Number of Units}

x1y1=x2y2\frac{x_1}{y_1} = \frac{x_2}{y_2} (The ratio remains constant)

💡Examples

Problem 1:

If 5 identical pens cost $15, how much will 8 of the same pens cost?

Solution:

$24

Explanation:

Step 1: Use the unitary method to find the cost of 1 pen (15÷5=15 \div 5 = 3). Step 2: Multiply the cost of 1 pen by the desired number of pens (3×8=3 \times 8 = 24).

Problem 2:

A recipe for 4 people requires 200g of flour. How much flour is needed for 10 people?

Solution:

500g

Explanation:

Step 1: Find the amount of flour per person (200g ÷\div 4 = 50g per person). Step 2: Multiply the flour per person by 10 people (50g ×\times 10 = 500g).

Problem 3:

A car travels 120 km in 2 hours at a constant speed. How far will it travel in 5 hours?

Solution:

300 km

Explanation:

Step 1: Calculate the distance covered in 1 hour (120 km ÷\div 2 = 60 km/h). Step 2: Multiply the distance per hour by 5 hours (60 km ×\times 5 = 300 km).