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If the ratio of b to c is 15 to 4, and the ratio of a to c is 3 to 7

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If the ratio of b to c is 15 to 4, and the ratio of a to c is 3 to 7 [#permalink]

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New post 11 May 2018, 00:32
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If the ratio of \(b\) to \(c\) is 15 to 4, and the ratio of \(a\) to \(c\) is 3 to 7, then what is the ratio of \(a\) to \(b\)?


A. \(\frac{3}{35}\)

B. \(\frac{4}{35}\)

C. \(\frac{1}{5}\)

D. \(\frac{1}{4}\)

E. \(\frac{7}{15}\)

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Re: If the ratio of b to c is 15 to 4, and the ratio of a to c is 3 to 7 [#permalink]

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New post 11 May 2018, 02:17
Bunuel wrote:
If the ratio of \(b\) to \(c\) is 15 to 4, and the ratio of \(a\) to \(c\) is 3 to 7, then what is the ratio of \(a\) to \(b\)?


A. \(\frac{3}{35}\)

B. \(\frac{4}{35}\)

C. \(\frac{1}{5}\)

D. \(\frac{1}{4}\)

E. \(\frac{7}{15}\)



\(\frac{a}{c}\) = \(\frac{3}{7}\)

\(\frac{b}{c}\) = \(\frac{15}{4}\)

Divide both the above fraction as below

\(\frac{a}{c}\) * \(\frac{c}{b}\)= \(\frac{3}{7}\) * \(\frac{4}{15}\)

\(\frac{a}{c}\) * \(\frac{c}{b}\) = \(\frac{4}{35}\)

Ans B
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Re: If the ratio of b to c is 15 to 4, and the ratio of a to c is 3 to 7 [#permalink]

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New post 11 May 2018, 09:21
Another way is to make value of C same in both the ratios and then divide:
b:c=15 : 4 And c:a=7 : 3,
b:c=15x7 : 4*7 And c:a=7*4 : 3*4
b:c= 105 : 28 And c:a=28 : 12
b:a=105 : 12
a:b=12/105=4/35
Just another way to do the question. It may seem a bit longer :)
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Re: If the ratio of b to c is 15 to 4, and the ratio of a to c is 3 to 7 [#permalink]

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New post 11 May 2018, 11:41
Bunuel wrote:
If the ratio of \(b\) to \(c\) is 15 to 4, and the ratio of \(a\) to \(c\) is 3 to 7, then what is the ratio of \(a\) to \(b\)?


A. \(\frac{3}{35}\)

B. \(\frac{4}{35}\)

C. \(\frac{1}{5}\)

D. \(\frac{1}{4}\)

E. \(\frac{7}{15}\)


a/b=(c/b)/(c/a)
a/b=(4/15)/(7/3)
a/b=4/35
B
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If the ratio of b to c is 15 to 4, and the ratio of a to c is 3 to 7 [#permalink]

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New post 11 May 2018, 13:02
Bunuel wrote:
If the ratio of \(b\) to \(c\) is 15 to 4, and the ratio of \(a\) to \(c\) is 3 to 7, then what is the ratio of \(a\) to \(b\)?


A. \(\frac{3}{35}\)

B. \(\frac{4}{35}\)

C. \(\frac{1}{5}\)

D. \(\frac{1}{4}\)

E. \(\frac{7}{15}\)

Another way: multiply.

\(\frac{b}{c}=\frac{15}{4}\)
\(4b = 15c\)

\(\frac{a}{c}=\frac{3}{7}\)
\(7a = 3c\)

Together:
\(4b = 15c\)
\(7a = 3c\)

Make the \(c\)'s equal. Multiply the second ratio by 5
\((7a*5 = 3c*5)\)
\(35a = 15c\)


Ratio of a : b ?
\(35a = 15c\)
\(4b = 15c\)

\(35a = 15c = 4b\)

\(35a = 4b\), thus

\(\frac{a}{b}=\frac{4}{35}\)


Answer B
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Re: If the ratio of b to c is 15 to 4, and the ratio of a to c is 3 to 7 [#permalink]

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New post 14 May 2018, 16:48
Bunuel wrote:
If the ratio of \(b\) to \(c\) is 15 to 4, and the ratio of \(a\) to \(c\) is 3 to 7, then what is the ratio of \(a\) to \(b\)?


A. \(\frac{3}{35}\)

B. \(\frac{4}{35}\)

C. \(\frac{1}{5}\)

D. \(\frac{1}{4}\)

E. \(\frac{7}{15}\)


We have the ratios:

b : c = 15 : 4

b : c = 105 : 28

And

a : c = 3 : 7

a : c = 12 : 28

Thus:

a : b = 12 : 105 = 4 : 35

Answer: B
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Re: If the ratio of b to c is 15 to 4, and the ratio of a to c is 3 to 7   [#permalink] 14 May 2018, 16:48
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