Ratio, Proportion and Variation

Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.

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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)

8 red and 12 blue marbles give 8:12. Both share a factor of 4, so 8:12 = 2:3. Ratios have no units.

Share 1200 in 1:3. Parts = 1+3 = 4, one part = 1200 ÷ 4 = 300. Shares are 300 and 900. Check: 300 + 900 = 1200.

3 pens cost 15, so k = 5 per pen and 6 pens cost 30. The graph is a straight line through the origin.

2 workers take 6 hours, so k = 12 worker-hours; 3 workers take 12 ÷ 3 = 4 hours. The graph is a hyperbola.

ratio	a comparison of two quantities of the same kind, written a : b
proportion	a statement that two ratios are equal, a : b = c : d
HCF	highest common factor, the largest number that divides each part exactly
constant of proportionality	the fixed number k linking the quantities, as in y = k x
direct proportion	as one quantity increases the other increases at the same rate; y = k x
inverse proportion	as one quantity increases the other decreases by the same factor; y = k/x
unitary method	finding the value of one unit first, then scaling to the amount needed
cross-multiply	multiply each numerator by the opposite denominator to solve a proportion

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