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What are the different formulas in Ration and Proportion for Class X ICSE?

Asked by tusharparik • 16 days ago

What are the different formulas in Ration and Proportion for Class X ICSE?

Answers

admin
16 days ago
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Mathematics - Ratio and Proportion Formulas for Class X ICSE

Here are the key formulas and concepts related to Ratio and Proportion for Class X ICSE:

Understanding Ratio and Proportion

Ratio: A ratio is a comparison of two quantities of the same kind. If 'a' and 'b' are two quantities, then the ratio is represented as a:b or a/b.

Proportion: A proportion is an equality of two ratios. If a:b = c:d, then a, b, c, and d are said to be in proportion.

Basic Formulas

  • Direct Proportion: If two quantities x and y are directly proportional, then x/y = k (where k is a constant). This means if x increases, y increases proportionally, and vice versa.
  • Inverse Proportion: If two quantities x and y are inversely proportional, then x * y = k (where k is a constant). This means if x increases, y decreases proportionally, and vice versa.

Properties of Proportion

  • Invertendo: If a:b = c:d, then b:a = d:c
  • Alternendo: If a:b = c:d, then a:c = b:d
  • Componendo: If a:b = c:d, then (a+b):b = (c+d):d
  • Dividendo: If a:b = c:d, then (a-b):b = (c-d):d
  • Componendo and Dividendo: If a:b = c:d, then (a+b):(a-b) = (c+d):(c-d)

Example Problems

Direct Proportion: If 5 kg of sugar costs ₹200, how much will 12 kg of sugar cost?
Solution: Let the cost be x. Then 5/200 = 12/x. Solving for x, x = ₹480.

Inverse Proportion: If 10 workers can build a wall in 12 days, how many days will 15 workers take to build the same wall?
Solution: Let the number of days be x. Then 10 * 12 = 15 * x. Solving for x, x = 8 days.

Key Tip: Understanding these formulas and their applications is crucial for solving problems related to ratio and proportion. Practice various types of problems to master these concepts.

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