CAT Quantitative Aptitude Questions | CAT Percentages Problems - Integers

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The question is from CAT Percentages. Solve this CAT Question from percentages to set the ball rolling. 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2019. This question is a very basic question that tests our understanding on the topic percentages using integers.

Question 4 : A earns 25% more than B. C earns 25% more than A. A earns 20% more than D. E earns 20% more than A. A, B, C, D, and E earn integer amounts less than Rs. 100. What is the total amount earned by all five of them put together?

  1. Rs. 300
  2. Rs. 245
  3. Rs. 305
  4. Rs. 480

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Explanatory Answer

Method of solving this CAT Question from Percentages: Compare the income of A, B, C and D.

A = \\frac{5}{4}\\) * B or B = \\frac{4}{5}\\) * A
C = \\frac{5}{4}\\) * A
A = \\frac{6}{5}\\) * D or D = \\frac{5}{6}\\) * A
E = \\frac{6}{5}\\) * A

In order for the amounts earned by A, B, C, D and E to be integers, the amount earned by A should be a multiple of 4, 5 and 6. Or, the amount earned by A should be a multiple of 60. The only multiple of 60 that is a 2–digit number is 60.
So, if A earns Rs. 60, B should earn Rs. 48. C should earn Rs. 75, D should earn Rs. 50 and E should earn Rs. 72.
The total income earned by all 5 of them should be equal to
Rs. 60 + Rs. 48 + Rs. 75 + Rs. 50 + Rs. 72 => Rs. 305

The question is " What is the total amount earned by all five of them put together?"
The total income earned by all 5 of them should be equal to Rs. 305

Hence, the answer is Rs. 305

Choice C is the correct answer.


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