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The ratio of w to x is 5 to 4. The ratio of x to y is 8 to 1

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The ratio of w to x is 5 to 4. The ratio of x to y is 8 to 1  [#permalink]

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New post 01 Jul 2014, 21:47
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The ratio of w to x is 5 to 4. The ratio of x to y is 8 to 1. If the ratio of y to z is 1 to 3, what is the ratio of w + x to z ?

A. 6:1
B. 8:1
C. 10:1
D. 24:1
E. 30:1

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Re: The ratio of w to x is 5 to 4. The ratio of x to y is 8 to 1  [#permalink]

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New post 02 Jul 2014, 00:22
Answer = A = 6:1

\(\frac{w}{x} = \frac{5}{4}\) .......... (1)

\(\frac{x}{y} =\frac{8}{1}\) ........... (2)

\(\frac{y}{z} = \frac{1}{3}\) ............. (3)

Applying componendo / dividendo to (1)

\(\frac{w+x}{x} = \frac{5+4}{4}\)

\(\frac{w+x}{x} = \frac{9}{4}\) ......... (4)

From (2) & (3),

x = 8y & \(y = \frac{z}{3}\)

So, \(x = \frac{8z}{3}\)............. (5)

Placing value of x from (5) in (4)

\(\frac{w+x}{\frac{8z}{3}} = \frac{9}{4}\)

\(\frac{3(w+x)}{8z}= \frac{9}{4}\)

\(\frac{w+x}{z} = \frac{9}{4} * \frac{8}{3} = 6\)

\(\frac{w+x}{z} = 6:1\)
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Re: The ratio of w to x is 5 to 4. The ratio of x to y is 8 to 1  [#permalink]

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New post 02 Jul 2014, 01:07
Gnpth wrote:
The ratio of w to x is 5 to 4. The ratio of x to y is 8 to 1. If the ratio of y to z is 1 to 3, what is the ratio of w + x to z ?

A. 6:1
B. 8:1
C. 10:1
D. 24:1
E. 30:1


\(\frac{w}{x}=\frac{5}{4}\)

and \(\frac{x}{y}=\frac{8}{1}\), so x=8y

w/x can be written as \(\frac{w}{x}=\frac{10}{8}\)

w=10/8x or 10y

z=3y

So \(\frac{10y+8y}{3y}= \frac{w+x}{z}\)

Ans 6:1--A
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Re: The ratio of w to x is 5 to 4. The ratio of x to y is 8 to 1  [#permalink]

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New post 02 Jul 2014, 07:41
Line the ratios up:

w:x
x:y
y:z

which is similar to:

5:4
8:1
1:3

Now, do some tweaking to make the value of x equal (because the value of y is already consistent)

10:8
8:1
1:3

Hence, w=10, x=8, y=1 and z=3

So,

w+x : z = 10 + 8 : 3 = 18 : 3 = 6 : 1

Correct Answer: A
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Re: The ratio of w to x is 5 to 4. The ratio of x to y is 8 to 1  [#permalink]

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New post 14 Jan 2018, 10:07
Gnpth wrote:
The ratio of w to x is 5 to 4. The ratio of x to y is 8 to 1. If the ratio of y to z is 1 to 3, what is the ratio of w + x to z ?

A. 6:1
B. 8:1
C. 10:1
D. 24:1
E. 30:1
Attachment:
Capture.PNG
Capture.PNG [ 2.25 KiB | Viewed 1864 times ]
So, w + x to z = \(\frac{(10 + 8)}{3}\) = 6 : 1, answer will be (A)
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Re: The ratio of w to x is 5 to 4. The ratio of x to y is 8 to 1  [#permalink]

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New post 17 Jan 2018, 07:25
Abhishek009 wrote:
Gnpth wrote:
The ratio of w to x is 5 to 4. The ratio of x to y is 8 to 1. If the ratio of y to z is 1 to 3, what is the ratio of w + x to z ?

A. 6:1
B. 8:1
C. 10:1
D. 24:1
E. 30:1
Attachment:
Capture.PNG
So, w + x to z = \(\frac{(10 + 8)}{3}\) = 6 : 1, answer will be (A)


Can any expert tell me if drawing such tables is the recommended approach?

Thank you
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Re: The ratio of w to x is 5 to 4. The ratio of x to y is 8 to 1 &nbs [#permalink] 17 Jan 2018, 07:25
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