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Assertion (A): The numbers 2, 6, 8, 24 are in proportion. Reason (R): Two ratios are in proportion when the product of the extremes equals the product of the means. Which is correct?

Class 6Ratio and ProportionRatio and Proportion
  • ABoth A and R are true, and R correctly explains A
  • BBoth A and R are true, but R does not explain A
  • CA is true but R is false
  • DA is false but R is true

Step-by-Step Solution

For 2 : 6 :: 8 : 24, extremes and means are equal, so they are in proportion (A is true). The rule stated in R is the correct test and explains A.
Answer: A) Both A and R are true, and R correctly explains A

Key idea: Proportion: when two ratios are equal

If a : , the four numbers are in proportion. The classic check: the **product of the extremes** equals the **product of the means** . Example: are 4 : 6 and 6 : 9 in proportion? Cross-multiply: . Equal → yes, in proportion.

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