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The ratio of two numbers a and b is 3:5. If 2 is added to both the numbers, the ratio becomes 2:3. Find b.

Correct answer: B. 10

  • A. 15
  • B. 10
  • C. 8
  • D. 5

Explanation

Let a = 3k and b = 5k. After adding 2 to each number, (3k + 2):(5k + 2) = 2:3, so 3(3k + 2) = 2(5k + 2), giving 9k + 6 = 10k + 4 and k = 2. Hence b = 5k = 10. The likely trap is option a, 15, which is the original ratio value if k is incorrectly taken as 3.

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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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