# CAT Practice : Percents, Profits

Percentages + algebra + Inequalities = Potent cocktail.

## Percentages - Variables

Q.14: A is x % more than B. B is y% less than C. If A, B and C are positive and A is greater than C, find the relation between x and y.
1. y (1 - x) < x
2. y (1 - x) > x
3. y (1 + x) < x
4. y (1 + x) > x

Choice C. y (1 + x) < x

## Detailed Solution

a = (1 + x) b
b = c (1 - y)
c = ${b \over 1 - y}$

a is greater than c
Or, b (1 + x) > ${b \over 1 - y}$
1 + x > ${1 \over 1 - y}$
(1 + x) (1 - y) > 1
1 + x - y - xy > 1
x > y (1 + x)
y < ${x \over 1 + x}$. Choice (C).

Correct Answer: y (1 + x) < x

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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,