In a certain neighborhood there are half as many beige house

Let x be the number of beige houses
Then number of white houses = 2x
Number of brown houses = 2x/5

Ratio of number of brown houses to number of beige houses = (2x/5)/(x) = 2:5

Option C

This is a pure ratio question, so there's no harm in picking a number for something if that makes things easier for you. If we have 10 white houses, we have 5 beige houses and 2 brown houses. So the answer is 2:5.

\(\frac{1}{2}*Be\) = \(1*W\)

\(5 * W\) = \(1*Br\) => \(\frac{1}{5}*Br\)

So Ration of Br to Be = \(\frac{1}{5}/\frac{1}{2}\) = \(\frac{2}{5}\)

Answer is C

Nave 81 - little correction

1/2 White =Be.House

&

white house =5 brown house .

translation : if there are 2 brown houses , there will be 10 white house : hence W.H=5 Brown House

therefore : 5/2 brown house =be.House
=> brown house/be.House =2/5

I usually do not have any problem with ratios.. but there are few which trouble me a lot. The above one use word 'as many'.

I read the problem and got the answer 5:2. I interpreted "half no. of beige = total no. of white & 5 times the no. of white = total no. of brown'.

The ans suggest otherwise. Could some one explain, how to interpret them correctly.

Thanks,

If I tell you, "I have five times as many problems as you do," what does it mean? Do I have more problems or do you?
I hope you will agree that I have more problems.
Similarly, I have half as many books as you means that I have fewer books.

Now look at the question:

"there are half as many beige houses as white houses" - implies Beige:White = 1:2 (There are fewer Beige houses)

"there are five times as many white houses as brown houses" - implies White:Brown = 5:1 (There are more White houses)

Hence, Beige:White:Brown = 5:10:2

Thanks for your reply. The moment you used the missing word 'times'. The problem was crystal clear. I will always assume the times word if not mentioned.

ex : 'half times'

Thanks karishma

I still don't get it . Are we multiplying both of the numbers in White to get the 10?

Karishma , just added a kudos for your reply.

As karishma stated :
"there are half as many beige houses as white houses" - implies Beige:White = 1:2 (There are fewer Beige houses)
"there are five times as many white houses as brown houses" - implies White:Brown = 5:1 (There are more White houses)

Hence, Beige:White:Brown = 5:10:2

She made the ratios common above
Be : Wi = 1:2 (same as 5:10)
Wi : br = 5:1 (same as 10:2)

Once the white ratio is made common in above 2 equations then we can merge the 2 as Be: wi : Br = 5:10:2

Another way to look at

Be/Wi = 1/2 ( Wi = 2 Be)
Wi/Br = 5/1 ( Wi = 5 Br)

so we 2 Be = 5 Br , Br/ Be = 2/5.

I hope I made some sense.

It is not difficult to concentrate on the stem and think: white is \(20\), brown is \(\frac{1}{5}\) of white so \(4\) and beige is \(half\) of white so \(10\)

\(Brown / beige\) \(=\)\(\frac{4}{10}\) \(=\) \(\frac{2}{5}\) C

30 seconds. that's it. no formula, no bother
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To add to what hikaps14 said, ratio between two numbers is nothing but the relation between them.

Beige:White = 1:2 means for every one Beige, there are two Whites

White: Brown = 5:1 means for every 5 Whites, there is 1 Brown.

So what is the relation between Beige and Brown? We don't know because the numbers of whites are not comparable. So what do we do? We make the Whites comparable i.e. we make them same.

Beige:White = 1:2 = 5:10 (ratio remains the same if you multiply each term by the same number) means for every 5 Beige, there are 10 Whites.
White: Brown = 5:1 = 10:2 means for every 10 WHites, there are 2 Browns.

Now we can say that for every 5 Beige, there are 10 Whites and for every 10 Whites, there are 2 Browns. SO for every 5 Beige, there are 2 Browns.

Beige:Brown = 5:2

This is how you manipulate ratios. It is useful to know.

This question is best solved taking numbers though (as done by Ian above)

Assume number of White houses as 10, Beige is half as many and White is 5 times Brown

Beige : White : Brown

5 : 10 : 2

Ratio of Brown to beige would be 2 : 5

Ans : C

White = W
Beige = W/2
Brown = W/5

So, Brown/Beige = (W/5)/(W/2) = 2/5

[quote="megafan"]In a certain neighborhood there are half as many beige houses as white houses and five times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses?

(A) 1:10

(B) 1:9

(C) 2:5

(D) 5:2

(E) 10:1

take Brown houses=100
then white houses =500
beige houses =250

ratio of brown houses/beige houses=100/250= 2:5
answer C

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