# CAT Quantitative Aptitude Questions | CAT Percentage Questions - Mixtures

###### CAT Questions | Percentages Problems| Percentage - Two digit numbers CAT Questions

The question is from CAT Percentages. CAT tests multiple ideas in the same question, and 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2022. Percentages is an important topic for CAT. In this question, a digit number and the number formed by reversing it's digits are compared with x. 10a + b and 10b + a, these two form a merry pair.

Question 12: A two digit number ab is 60% of x. The two-digit number formed by reversing the digits of ab is 60% more than x. Find x.

1. 45
2. 54
3. 63
4. 72

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##### Method of solving this CAT Question from Percentages - Two digit numbers: This question is all about forming the right equations.

10a + b = 0.6x
10b + a = 1.6x
Subtracting one from the other, we have
9b - 9a = x or x = 9 (b - a)
x should be a multiple of 9.
10a + b = 3x/5 this implies that x should also be a multiple of 5.Or, x should be a multiple of 45
x should be equal to 45, ab = 27, ba = 72

The question is "The two-digit number formed by reversing the digits of ab is 60% more than x. Find x."
x should be equal to 45

##### Hence, the answer is 45.

Choice A is the correct answer.

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