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CAT 2019 Quant Question with Solution 37

Question:
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. 24
  2. 26
  3. 32
  4. 35
Show Answer

Correct Answer: Option: 3

Let their scores after review be 11x, 10x, and 3x respectively.

Therefore, their scores before review was: (11x-6), 10x-6) and (3x-6) respectively.

Given, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali.

$\Rightarrow \left( 3x-6 \right)=\frac{1}{12}\left[ \left( 11x-6 \right)+\left( 10x-6 \right) \right]$

$\Rightarrow 12\left( 3x-6 \right)=21x-12$

$\Rightarrow 36x-72=21x-12$

$\Rightarrow 36x-21x=72-12=60$

$\Rightarrow x=4$

Now, Anjali’s score – Rama’s score = (11x-6)-(3x-6)=8x =32.


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