# CAT Practice : Percents, Profits

Add x and y to simple topics and then they take a sinister hue. This question is a classic example.

## Percentages - Variables

Q.2: P is x% more than Q. Q is (x - 10)% less than R. If P > R, what is the range of values x can take?
1. 10% to 28%
2. 10% to 25%
3. 10% to 37%
4. 10% to 43%

Choice C. 10% to 37%

## Detailed Solution

P = $Q {({1} {+} {x \over 100})}$
Q = $R {({1} {-} {x - 10 \over 100})}$
R = ${Q \over {{1} {-} {x-10 \over 100}}}$

P > R
$Q {({1} {+} {x \over 100})}$ > ${Q \over {{1} {-} {x - 10 \over 100}}}$
${1} {+} {x \over 100}$ > ${1 \over {100 - x + 10 \over 100}}$
${100 + x \over 100}$ > ${100 \over 110 - x}$
(100 + x) (110 – x) > 100 x 100
11,000 + 110x – 100x – x2 > 10000
1000 + 10x – x2 > 0
x2 – 10x – 1000 < 0
x2 – 10x + 25 < 1000 + 25
(x – 5)2 < 1025
x – 5 < 32
x < 37
x could range from 10% to 37%

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## More questions from Averages, Ratios, Mixtures

A number of beautiful questions from three allied topics. Most sportsmen will tell you - If you know the percentage play, you can profit well from it,