# CAT Practice : Percents, Profits

When x's and y's get thrown about, questions always seem harder. But knowing how to deal with these is very crucial.

## Percentages - Variables

Q.7: A is x% less than B, A is y% less than C. C is k% more than B. Express k in terms of x and y.
1. ${(y - x)100 \over 100 - y}$
2. ${(y + x)100 \over 100 - y}$
3. ${(y - x)100 \over 100 - x}$
4. ${(y - x)100 \over 100 + y}$

Choice A. ${(y - x)100 \over 100 - y}$

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## Detailed Solution

A = $B{({1} {-} {x \over 100})}$    -------- Equation (1)
A = $C{({1} {-} {y \over 100})}$    -------- Equation (2)
C = $B{({1} {+} {k \over 100})}$    -------- Equation (3)

Substituting equations (1) and (3) in (2), we get
${B{({1} {+} {k \over 100})} {({1} {-} {y \over 100})} {=} {B{({1} {-} {x \over 100})}}}$
${{1} {+} {k \over 100} {-} {y \over 100} {-} {ky \over 100^2} {=} {1} {-} {x \over 100}}$
${k \over 100} {({1} {-} {y \over 100})} {=} {({y - x \over 100})}$
k = ${({(y − x) 100 \over 100 - y})}$. Answer Choice (A)

Correct Answer: ${(y - x)100 \over 100 - y}$

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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,