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Ratio of scores after revision

CAT 2019 Slot 2 · Quantitative Ability · Medium · Ratio & proportion

This is a medium Quantitative Ability question from the CAT 2019 Slot 2 paper. It tests Ratio & proportion. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by 6. The revised scores of Anjali, Mohan, and Rama were in the ratio 11:10:3. Then Anjali's score exceeded Rama's score by

  1. A.

    26

  2. B.

    32

  3. C.

    24

  4. D.

    35

Answer

B

Explanation

Let the revised scores of Anjali, Mohan, and Rama be 11x,10x,11x, 10x, and 3x3x respectively. Their original scores were 11x−6,10x−6,11x - 6, 10x - 6, and 3x−63x - 6.

Given that Rama's original score was 112\frac{1}{12} of the sum of Mohan's and Anjali's original scores: 3x−6=112[(10x−6)+(11x−6)]3x - 6 = \frac{1}{12} [(10x - 6) + (11x - 6)] 12(3x−6)=21x−1212(3x - 6) = 21x - 12 36x−72=21x−12  ⟹  15x=60  ⟹  x=436x - 72 = 21x - 12 \implies 15x = 60 \implies x = 4

Anjali's original score =11(4)−6=38= 11(4) - 6 = 38. Rama's original score =3(4)−6=6= 3(4) - 6 = 6. Difference =38−6=32= 38 - 6 = 32.

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