# CAT Practice : Percents, Profits

10a + b and 10b + a, these two form a merry pair.

## Percents - Two digit numbers

Q.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

Choice A. 45

## Detailed Solution

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 = ${3x \over 5}$ 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

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