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Three numbers are in the ratio 3:4:5 and their L.C.M is 2400. Their H.C.F is:

Correct answer: A. 40

  • A. 40
  • B. 80
  • C. 120
  • D. 200

Explanation

Write the numbers as 3x, 4x and 5x. Since 3, 4 and 5 are pairwise coprime, their LCM is 3 x 4 x 5 x = 60x; hence 60x = 2400, so x = 40. Their HCF is therefore 40. The likely mistake is choosing 80 by taking an incomplete common factor from the LCM calculation.

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Ratios compare quantities in the same units, while proportions state that two ratios are equal. Problems cover simplification, division in a given ratio, direct and inverse variation, scale, and missing terms, with attention to the difference between a ratio and a fraction representing part of a whole.

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