Question

There are 10 children in a room. The ratio of boys to girls increased when another boy and another girl entered the room. What is the greatest number of boys that could originally have been in the room?
A. 1
B. 4
C. 5
D. 9
E. 10

Answer 1

x/10-x initial ratio 0<=x<10
x+1/10-x+1 final ratio
x/10-x < x+1/11-x
Taking only numerator x(11-x)-(x+1)(9-x) denominator will always be >0 (Hint check the range of x)
11x -x^2 -9x -9 +x^2 > 0
2x -11 > 0
x > 5.5

Answer 2

\[\frac{4}{6} \approx 66\%\]
\[\frac{5}{7} \approx 71\%\]

Answer 3

Calculation mistake :(
11x -x^2 -8x -9 +x^2 > 0
4x -9> 0
x > 9/4
so x can start from 3

Answer 4

It's better in this case to calculate using actual numbers.

Answer 5

Clearly the initial ratio that works is

\[\frac{\text{boys}}{\text{girls}} = \frac{4}{6}\]

Answer 6

Because if you increase each by one you get \(\large\frac{5}{7}\) and \[\frac{5}{7} > \frac{4}{6}\]

Answer 7

Is it only me or you guys are facing difficulty in viewing text written from equation tab?
I am seeing \(\large\frac{5}{7}\) and \[\frac{5}{7} > \frac{4}{6}\] It is not parsed properly

Answer 8

\[B+G=10\]
\[B=10-G\]
\[\frac{ B+1 }{ G+1 }>\frac{ B }{ G }\]
\[\frac{10-G+1}{G+1}> \frac{10-G}{G}\]
\[G(11-G)>(10-G)(G+1)\]
\[11G-G^{2}>9G-G^{2}+10\]
\[11G>9G+10\]
\[2G>10\]
\[G>5\]
So G=6,B=10-G=4
Ans. 4

Answer 9

Thanks everyone .. But I'm a little confused...

Answer 10

@ybarrap that's great if you want to do more work than you need to.

Answer 11

In addition to confusing the user

Answer 12

@ankit042 , I'm able to view everything just fine. What browser are you using?

Answer 13

Thanks to everyone. I understand now :)

Answer 14

np

Answer 15

Which explanation did you understand?

Answer 16

I think that she just understood that the answer is 4.

Answer 17

I am using chrome Version 28.0.1500.71 on ubuntu 12.04

Answer 18

I'm using Chrome...same version so it must be the unbuntu.

Answer 19

hmm maybe! It used to work before though!

Answer 20

Refresh the page. This may refresh the java libraries associated with LaTex

Answer 21

I understood @ybarrap's explanation