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

If a = 4 and b = 5, what is the value of (a+b)^2?

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If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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A man spends 75% of his income and saves Rs. 600. What is his total income?

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If sin(A) = 1/2 and A is acute, what is the value of A?

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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What is the slope of a line passing through the points (2, 3) and (4, 7)?

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If 8x = 512, what is the value of x?

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What is the sum of the first 50 positive integers?

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If a number is divisible by 9, it is also divisible by which of the following?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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