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A stationery shop has 45 blue pens and 27 black pens. Write the ratio of black pens to blue pens in its simplest form.

Class 6Ratio and ProportionRatio and Proportion
  • A5 : 3
  • B3 : 5
  • C9 : 15
  • D3 : 8

Step-by-Step Solution

Black : blue = 27 : 45. HCF of 27 and 45 is 9, so 27÷9 : 45÷9 = 3 : 5. Writing 5 : 3 puts blue first, but the order asked for was black first. 9 : 15 is equivalent yet not simplest, and 3 : 8 is black : total (27 : 72).
Answer: B) 3 : 5

Key idea: Equivalent ratios and simplest form

Just like equivalent fractions: multiply or divide both parts of a ratio by the same non-zero number to get an equivalent ratio. 2 : 3 = 4 : 6 = 6 : 9 = 20 : 30. The **simplest form** is when the two parts share no common factor other than 1. So 20 : 30 simplifies (divide both by 10) to 2 : 3.

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