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# The local bowling alley has three categories of bowlers; beginner, int

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Math Expert
Joined: 02 Sep 2009
Posts: 52168
The local bowling alley has three categories of bowlers; beginner, int  [#permalink]

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27 Dec 2017, 01:28
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Difficulty:

15% (low)

Question Stats:

88% (01:50) correct 13% (02:52) wrong based on 50 sessions

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The local bowling alley has three categories of bowlers; beginner, intermediate and expert. If there are 6 beginning bowlers for every 5 intermediate bowlers and 5 beginning bowlers for every expert bowler, what is the ratio of intermediate bowlers to all bowlers?

A. 30 : 61
B. 25 : 61
C. 25 : 54
D. 1 : 4
E. 1 : 3

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Posts: 64
Re: The local bowling alley has three categories of bowlers; beginner, int  [#permalink]

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27 Dec 2017, 03:58
let the number of different types of bowlers be b,i,e (for beginning bowlers, intermediate bowlers, expert bowler respectively)
there are 6 beginning bowlers for every 5 intermediate bowlers => b= 6x; i=5x
5 beginning bowlers for every expert bowler => b= 5y; e=y
=> 5y=6x => y=6x/5 => e=6x/5

Required ratio = i/(b+i+e) = 5x /(6x+5x+6x/5)
= 25x/(55x+6x)
=25/61
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Re: The local bowling alley has three categories of bowlers; beginner, int  [#permalink]

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27 Dec 2017, 10:26
Bunuel wrote:
The local bowling alley has three categories of bowlers; beginner, intermediate and expert. If there are 6 beginning bowlers for every 5 intermediate bowlers and 5 beginning bowlers for every expert bowler, what is the ratio of intermediate bowlers to all bowlers?

A. 30 : 61
B. 25 : 61
C. 25 : 54
D. 1 : 4
E. 1 : 3
Attachment:

Ratio.PNG [ 2.96 KiB | Viewed 480 times ]
Total number of bowlers is 30+25+6 = 61

So, the ratio of intermediate bowlers to all bowlers is $$25:61$$

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Abhishek....

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The local bowling alley has three categories of bowlers; beginner, int  [#permalink]

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27 Dec 2017, 15:04
Abhishek009 wrote:
Bunuel wrote:
The local bowling alley has three categories of bowlers; beginner, intermediate and expert. If there are 6 beginning bowlers for every 5 intermediate bowlers and 5 beginning bowlers for every expert bowler, what is the ratio of intermediate bowlers to all bowlers?

A. 30 : 61
B. 25 : 61
C. 25 : 54
D. 1 : 4
E. 1 : 3
Attachment:
Ratio.PNG
Total number of bowlers is 30+25+6 = 61

So, the ratio of intermediate bowlers to all bowlers is $$25:61$$

Hi Abhishek,

The answer is B not C. I have marked that with RED text.
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Re: The local bowling alley has three categories of bowlers; beginner, int  [#permalink]

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27 Dec 2017, 17:12
Bunuel wrote:
The local bowling alley has three categories of bowlers; beginner, intermediate and expert. If there are 6 beginning bowlers for every 5 intermediate bowlers and 5 beginning bowlers for every expert bowler, what is the ratio of intermediate bowlers to all bowlers?

A. 30 : 61
B. 25 : 61
C. 25 : 54
D. 1 : 4
E. 1 : 3

$$Beginner=b;Intermediate=i;Expert=e$$

What is $$\frac{i}{(b+i+e)}?$$

$$6b=5i$$, so $$\frac{i}{b}=\frac{5x}{6x}$$ and $$e=5b$$ so $$\frac{e}{b}=\frac{y}{5y}$$

Least common multiple of $$b=6x$$ and $$b=5y$$ is $$30$$.

Multiples $$x$$ and $$y$$ will merge to $$z$$.

New ratio $$i:b:e=[5x*(5):(30x=30y):y*(6)]=25z:30z:6z$$

Substitute values for $$i,b,e$$: $$\frac{i}{(b+i+e)}=\frac{25z}{30z+25z+6z}=\frac{25z}{61z}=25:61$$

Re: The local bowling alley has three categories of bowlers; beginner, int &nbs [#permalink] 27 Dec 2017, 17:12
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