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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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Math Expert
Joined: 02 Sep 2009
Posts: 45302
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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11 May 2018, 00:32
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Question Stats:

88% (00:59) correct 12% (00:36) wrong based on 33 sessions

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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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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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Sudhanshu

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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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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
Director
Joined: 07 Dec 2014
Posts: 998
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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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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Joined: 22 May 2016
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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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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

$$\frac{a}{b}=\frac{4}{35}$$

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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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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

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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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