2:1

Do you mean the ratio 2:1? If so, here’s a quick refresher you can use on exams.

What 2:1 means

• A:B = 2:1 means A = 2k and B = 1k for some common factor k.
• Total parts = 2 + 1 = 3 parts.
• Fractions: A = 2/3 of the total, B = 1/3 of the total.
• Percentages: A ≈ 66.67%, B ≈ 33.33%.

Common problems

• If total quantity T is given:
  • A = (2/3)T, B = (1/3)T
• If A:B = 2:1 and A is known:
  • A = 2B, so B = A/2
• If A:B = 2:1 and A + B = T:
  • 3 parts total, A = (2/3)T, B = (1/3)T
• If you’re given raw amounts and want the ratio:
  • Example: A = 40, B = 20 → ratio simplifies to 2:1
• If you’re given a different pair but need to scale:
  • To scale by factor k: A = 2k, B = k

Practice

1. If A:B = 2:1 and A + B = 90, what are A and B?
   • A = 2/3 of 90 = 60, B = 30.
2. A = 28 and A:B = 2:1. What is B?
   • B = A/2 = 14.
3. Find the percentage of the mixture that is B if A:B = 2:1.
   • B = 1 part out of 3 parts = 1/3 ≈ 33.33%.

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