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# For any positive x, y and z if x is n% of y and z is m% of y

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Intern
Joined: 18 Feb 2014
Posts: 24
For any positive x, y and z if x is n% of y and z is m% of y  [#permalink]

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13 Jun 2014, 00:37
1
9
00:00

Difficulty:

65% (hard)

Question Stats:

62% (01:19) correct 38% (01:21) wrong based on 189 sessions

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For any positive x, y and z if x is n% of y and z is m% of y then what percentage must x be of z?
A. (n/m)%
B. (m × n)%
C. (100 / [m × n]) %
D. (100 × m/n)%
E. (100 × n/m)%
Math Expert
Joined: 02 Sep 2009
Posts: 49300
Re: For any positive x, y and z if x is n% of y and z is m% of y  [#permalink]

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13 Jun 2014, 01:18
hapless12 wrote:
For any positive x, y and z if x is n% of y and z is m% of y then what percentage must x be of z?
A. (n/m)%
B. (m × n)%
C. (100 / [m × n]) %
D. (100 × m/n)%
E. (100 × n/m)%

x is n% of y: $$x=\frac{n}{100}*y$$;

z is m% of y: $$z=\frac{m}{100}*y$$;

What percentage must x be of z: $$\frac{x}{z}*100=\frac{n}{m}*100$$.

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Joined: 02 Sep 2009
Posts: 49300
Re: For any positive x, y and z if x is n% of y and z is m% of y  [#permalink]

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13 Jun 2014, 01:19
1
Bunuel wrote:
hapless12 wrote:
For any positive x, y and z if x is n% of y and z is m% of y then what percentage must x be of z?
A. (n/m)%
B. (m × n)%
C. (100 / [m × n]) %
D. (100 × m/n)%
E. (100 × n/m)%

x is n% of y: $$x=\frac{n}{100}*y$$;

z is m% of y: $$z=\frac{m}{100}*y$$;

What percentage must x be of z: $$\frac{x}{z}*100=\frac{n}{m}*100$$.

Similar questions to practice: if-25-percent-of-p-is-equal-to-10-percent-of-q-and-pq-0-th-168485.html
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Re: For any positive x, y and z if x is n% of y and z is m% of y  [#permalink]

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16 Jun 2014, 04:43
2
hapless12 wrote:
For any positive x, y and z if x is n% of y and z is m% of y then what percentage must x be of z?
A. (n/m)%
B. (m × n)%
C. (100 / [m × n]) %
D. (100 × m/n)%
E. (100 × n/m)%

x is n% of y MEANS x= (n/100 )* y------------------------eq1

z is m% of y MEANS z= (m/100 )* y------------------------eq2

Find equation of x & z
substitute value of y from 2nd equation into Ist equation
so x= (n/100)*(100z/m)
so x= (n/m)z
or x= (100n/m)z/100
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Re: For any positive x, y and z if x is n% of y and z is m% of y  [#permalink]

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22 May 2017, 18:44
hapless12 wrote:
For any positive x, y and z if x is n% of y and z is m% of y then what percentage must x be of z?
A. (n/m)%
B. (m × n)%
C. (100 / [m × n]) %
D. (100 × m/n)%
E. (100 × n/m)%

We are given:

x = (n/100)y

x/(n/100) = y

100x/n = y

AND

z = (m/100)y

z/(m/100) = y

100z/m = y

We can equate our two equations and then express x as a percentage of z:

100x/n = 100z/m

100x/100z = not n/m

x/z = n/m

Thus, x/z * 100 = n/m * 100.

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Re: For any positive x, y and z if x is n% of y and z is m% of y  [#permalink]

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01 Jul 2018, 17:19
X=n/100 y
Z=m/100 y
X=n/100*100z/m
X=n/m z

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Re: For any positive x, y and z if x is n% of y and z is m% of y &nbs [#permalink] 01 Jul 2018, 17:19
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