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If 45% of z is 120% of y and y is 75% of x, what percent of x is z? 04 Aug 2015, 23:44
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A
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45% (medium)

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69% (02:05) correct 31% (02:13) wrong based on 959 sessions

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If 45% of z is 120% of y and y is 75% of x, what percent of x is z?

A. 200
B. 160
C. 100
D. 65
E. 50
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A
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If 45% of z is 120% of y and y is 75% of x, what percent of x is z? 05 Aug 2015, 06:53
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shyind
If 45% of z is 120% of y and y is 75% of x, what percent of x is z?


A. 200
B. 160
C. 100
D. 65
E. 50
Show more

(45/100)z = (120/100)y

and y = (75/100)x i.e. y = (3/4)x

i.e. (45/100)z = (120/100)*(3/4)x

i.e. z = (120*3)x/(45*4)

i.e. z = (2)x = (200/100)x

i.e. z is 200% of x

Answer: Option A
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If 45% of z is 120% of y and y is 75% of x, what percent of x is z? 08 Feb 2020, 07:56
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shyind
If 45% of z is 120% of y and y is 75% of x, what percent of x is z?

A. 200
B. 160
C. 100
D. 65
E. 50
Show more

Another approach is to find values that satisfy the given information.

y is 75% of x
So it could it be the case x = 400 and y = 300

45% of z is (equals) 120% of y
120% of y = (1.2)(300) = 360
So, 45% of z = 360
In other words, 0.45z = 360
Divide both sides by 0.45 to get: z = 800

What percent of x is z?
In other words: What percent of 400 is 800?
Another way to phrase this is: 800 is what percent of 400?
Since 800 is TWICE 400, we can also conclude that 800 is 200 percent of 400

Answer: A

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If 45% of z is 120% of y and y is 75% of x, what percent of x is z? 19 Apr 2020, 04:49
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shyind
If 45% of z is 120% of y and y is 75% of x, what percent of x is z?

A. 200
B. 160
C. 100
D. 65
E. 50
Show more

We can create the equations:

0.45z = 1.2y

and

y = 0.75x

We need to determine the value of z/x * 100.

Solving the first equation, we have:

y = 0.45z/1.2 = 4.5z/12 = 9z/24 = 3z/8

Substituting y = 3z/8 into the second equation, we have:

3z/8 = 0.75x

3z/8 = 3x/4

z/x = 3/4 * 8/3

z/x = 2

Therefore, z/x * 100 = 2 * 100 = 200.

Answer: A
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If 45% of z is 120% of y and y is 75% of x, what percent of x is z? 10 Jul 2021, 09:24
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45% of z is 120% of y: \(\frac{45}{100} * z = \frac{120}{100} * y\)

=> \(z = \frac{120}{45} * y = \frac{8y}{3} \)


y is 75% of x: \(y = \frac{75}{100} * x \)

=> \(x = \frac{4y}{3 }\)

What percent of x is z: Let say 'p' percent of 'x' is 'z'.

=> \(\frac{p}{100} * x = z\)

=> \(\frac{p}{100} * \frac{4y}{ 3} = \frac{8y}{3} \)

=> p = 100 * 2 = 200

Answer A
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If 45% of z is 120% of y and y is 75% of x, what percent of x is z? 10 Jul 2021, 09:38
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Asked: If 45% of z is 120% of y and y is 75% of x, what percent of x is z?

45%*z = 120%*y
y = (45%/120%)*z = 3z/8
y = 75%*x = 3x/4 = 3z/8
z = 2x = 200% *x

IMO A
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If 45% of z is 120% of y and y is 75% of x, what percent of x is z? 10 Jul 2021, 09:41
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45% = 9/20
120% = 6/5
75%. = 3/4

Since LCM is 20.



So as per Question stem
\(9/20z = 6/5*y\) or 3z = 8y
\(Y = 15/20*x\) or 4y = 3x

Since 3z= 8y and 4y = 3x then
8y = 6x = 3z

Hence x is 200 percent of z \(( 6/3*100 )\)

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If 45% of z is 120% of y and y is 75% of x, what percent of x is z? 27 Oct 2022, 21:54
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If 45% of z is 120% of y and y is 75% of x, what percent of x is z?

A. 200
B. 160
C. 100
D. 65
E. 50

We could use ratios
If 45% of z is 120% of y = \(9/20Z\) = \(6/5Y\) Make denominators equal\( 9/20Z\) = 24/20Y - 9Z = 24Y - \(Z/Y\) = \(24/9\)
y is 75% of x = Y =\(3/4X\) \(X/Y\) = \(4/3\) (Multiply denominator and numerator by 3 to make denominator 9) \(X/Y\) = \(12/9\)

what percent of x is z - \(?/100\) * 12 = 24 = \(24/12\) * 100 = 200

A
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If 45% of z is 120% of y and y is 75% of x, what percent of x is z? 17 Nov 2025, 19:07
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