    Question

# A person increases a number by x% and then decreases it by y%. Increases it again by x% and then again decreased by y%. The resultant number is z% more than the original number. If x,y and z are all positive numbers then which of the following are not possible?

A
x=y
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B
x>y
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C
x<y
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D
xy
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Solution

## The correct options are B x=y C x<y D x≥yLet the no. be nAfter increase by x% it becomes (100+x)%×n=n(1+x100)After decrease by y% it becomes (100−y)(100+x)%×n=n(1+x100)(1−y100)Increasing again by x% and decreasing by y% we get new number n0=n(1+x100)2(1−y100)2Given that n0=(100+z)%×n=n(1+z100)⟹(1+z100)=(1+x100)2(1−y100)2⟹(1+z100)=[(1+x100)(1−y100)]2⟹(z100)=[(1+x−y100)−(xy100)]2−1⟹(z100)=[(x−y100)−(xy100)][2+x−y100−xy1000]We know that 0≤x≤100 and 0≤y≤100⟹ z will be negative.Hence x=y is not possible.Similarly x<y is not possible.Hence x<y,x=y,x≥y is not possible.  Suggest Corrections  0      Similar questions  Related Videos   Percentages and Why Percentages
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