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CAT 2019 Quant Question with Solution 7

Ramesh and Gautam are among 22 students who write an examination. Ramesh scores 82.5. The average score of the 21 students other than Gautam is 62. The average score of all the 22 students is one more than the average score of the 21 students other than Ramesh. The score of Gautam is

  1. 49
  2. 48
  3. 51
  4. 53
Show Answer

Correct Answer: Option: 3

Let Gautam’s score be g. Also, let x be the average of all 22 students so that the total scores of all 22 students =22x.

From the first condition:

22x-g = 21×62 … (1)

From the second condition:

$\begin{align} & 22x\text{ }-82.5\text{ }=\text{ }21\left( x-1 \right) \\ & \Rightarrow 22x-21x=82.5-21 \\ & \Rightarrow x=61.5 \\ \end{align}$

Putting x=61.5 in (1), we get g = 51.

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