Fwd: Puzzle: Color balls

[Vikram Agrawal (विक्रम अग्रवाल)]

-vicky
विक्रम अग्रवाल

---------- Forwarded message ----------
From: Vikram Agrawal (विक्रम अग्रवाल) <v.r.a...@gmail.com>
Date: Sun, Oct 16, 2011 at 12:45 PM
Subject: Puzzle: Color balls
To: cotpi <puz...@cotpi.com>

There are two baskets containing the same number of balls. Each ball is either red or blue. The percentage of red balls in the first basket rounded off to the nearest tenth is 34.2%. The number of red balls in the second basket is 11. Which basket has more red balls?

 

 

Ratio of red ball to blue balls in first basket. 34.2/65.8 = .52 = 13/25. So 13 out of 38 balls will give 34.2% red balls. But, does less no of balls give this?

 

Now 34.2% is just more than 33.3% = .9% diff. To satisfy 34.2% condition x/(3x-1)-0.333 should give .009 or divisor of same (x = no of red balls).

13/38 - 13/39 = .009

but x/(3x-1) - 0.333 <? (x -1)/(3x-4) - 0.333

x/(3x-1) - (x-1)/(3x-4) <? 0

3x^2 - 4x - 3x^2 + 3x - 3x  -1 <? 0

-4x  -1 < 0 for all x >= 0

hence,

x/(3x-1) - 0.333 < (x -1)/(3x-4) - 0.333

 

Thus reducing number of ball will increase the diff between .33 and next bigger ratio hence can't get diff of 0.009.

For 12 red balls diff 0.010 so rounding off to 0.001 can't make both same. (Red ball ratio of 34.3 rounded off).

 

So first basket has atleast 13 red balls more than second with has 11.

 

-Vikram

 

-vicky
विक्रम अग्रवाल

[Susam Pal]

> There are two baskets containing the same number of balls. Each ball is
> either red or blue. The percentage of red balls in the first basket rounded
> off to the nearest tenth is 34.2%. The number of red balls in the second
> basket is 11. Which basket has more red balls?
>
> Ratio of red ball to blue balls in first basket. 34.2/65.8 = .52 = 13/25. So
> 13 out of 38 balls will give 34.2% red balls. But, does less no of balls
> give this?
>
> Now 34.2% is just more than 33.3% = .9% diff. To satisfy 34.2% condition
> x/(3x-1)-0.333 should give .009 or divisor of same (x = no of red balls).
> 13/38 - 13/39 = .009
> but x/(3x-1) - 0.333 <? (x -1)/(3x-4) - 0.333
> x/(3x-1) - (x-1)/(3x-4) <? 0
> 3x^2 - 4x - 3x^2 + 3x - 3x  -1 <? 0
> -4x  -1 < 0 for all x >= 0
> hence,
> x/(3x-1) - 0.333 < (x -1)/(3x-4) - 0.333
>
> Thus reducing number of ball will increase the diff between .33 and next
> bigger ratio hence can't get diff of 0.009.
> For 12 red balls diff 0.010 so rounding off to 0.001 can't make both same.
> (Red ball ratio of 34.3 rounded off).
>
> So first basket has atleast 13 red balls more than second with has 11.
>
> -Vikram
>
> -vicky
> विक्रम अग्रवाल

The conclusion is correct. The reasoning is correct as well except one
step.

x(3x - 4) - (x - 1)(3x - 1) isn't -4x - 1. It is -1.

http://www.wolframalpha.com/input/?i=x(3x+-+4))+-+(x+-+1)(3x+-+1)