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

What is the sum of the first 50 positive integers?

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A number is increased by 20% and then decreased by 10%. What is the net change?

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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 perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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What is the HCF of 48 and 180?

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If two complementary angles differ by 30°, what are the angles?

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If 2x = 16, what is the value of x?

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