Multiple choice

In two blends of mixed tea, the ratios of Darjeeling and Assam tea are 4:7 and 2:5. The ratio in which these two blends should be mixed to get the ratio of Darjeeling and Assam tea in the new mixture as 6:13 is.

  1. 27: 38

  2. 22: 27

  3. 35: 22

  4. 27: 22

  5. 22: 35
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E Correct answer
Explanation

Let the blends be mixed in ratio x:y. First blend: Darjeeling fraction = 4/11, Assam = 7/11. Second blend: Darjeeling = 2/7, Assam = 5/7. Final mixture: Darjeeling = 6/19, Assam = 13/19. Using allegation: (4/11)x + (2/7)y / (x+y) = 6/19. Cross-multiply: 19(4/11)x + 19(2/7)y = 6x + 6y. Solving gives x:y = 22:35. Verify: (4/11)(22) + (2/7)(35) = 8 + 10 = 18, and (7/11)(22) + (5/7)(35) = 14 + 25 = 39, ratio 18:39 = 6:13.

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