Topic Details (Notes format)

How to Solve Proportions (Cross-Multiplication)

Subject: Mathematics

Book: Maths Mastery

Proportions equate two ratios, like a/b = c/d. Cross-multiplication states ad = bc. For example, if 2/5 = x/15, then 2 × 15 = 5 × x, meaning 30 = 5x, so x = 6. Proportions answer real-world questions: “If 2 liters costs ₹100, what does 5 liters cost?” or “If 3 out of 10 students prefer a subject, how many out of 50 might prefer it?” The technique is vital for scaling recipes, resizing images, or solving geometry similarity. Consistent practice ensures you can set up and solve ratio-based statements in a single, efficient step.

Practice Questions

The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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If 5x - 2 = 13, what is the value of x?

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A number is increased by 20% and then decreased by 20%. What is the net change?

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The LCM of 12 and 15 is:

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If the average of five consecutive odd numbers is 25, what is the largest number?

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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What is the sum of the first 20 odd numbers?

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